All the World's a Stage
This guide is written as a follow up to numerous RP experiences as a blood elf; a large amount of players seem to have misconceptions as to what a blood elf actually is, and how they behave.
No one can tell you exactly how to roleplay anything, so take below as a helping hand and a guide - not a rulebook.
The blood elves, like many other races, have a shared experience that binds them together as a people: that of the Scourge invasion, and the almost total destruction of Quel'Thalas. However, the blood elves are different to the other races in several respects, which makes them much closer as a people. The only other race that is closer as a people are their cousins the night elves (night elves regard one another as brother and sister, are pretty much all friends, and so on- blood elves are more vicious and will kill other members of their race more likely than night elves by far if they feel it is warranted or are "bad guys").
Firstly, the Scourge invasion happened almost 20 years ago now following MoP. Secondly, 75% of the population died. The survivors faced two grueling tasks - burning their beloved homeland to convince the Scourge to leave, and fighting a heroic last stand on Sunstrider Isle.
What does this mean for your character's general demeanor and personality? Well, unless they have a very, very good reason to be, they are not going to be very happy. Chance are very high that they will have lost a large number of friends and family in the conflict, and the high elven seclusion and long lifetimes mean this will be quite difficult for them to deal with. This means that any overtly happy blood elves are likely to be regarded as either insane or fanatical devotees of Kael'thas. This is a key point to remember: by being a blood elf, you have to have taken part in this conflict, and so you will bear the scars. There isn't much scope for developing a blood elf without including some reference to this event.
The blood elf society is largely run by the Magisters, who are overwhelmingly autocratic and arguably totalitarian. Their Arcane Guardians keep the peace by unthinking force, and any dissenters are mind controlled into fitting in.
This has several key ramifications, especially when roleplaying within Silvermoon City itself.
Firstly, you are unlikely to criticize the City or the Government brazenly and in public places, such as the inn. Nor are you likely to declare that this is a free country and you can say what you like. You live in an oppressive nation, and will have to express any dissenting opinions outside of Silvermoon or in secluded places, away from the paths of the Arcane Guardians.
Secondly, unless you are a mage, you are unlikely to hold power. This is something that RPers with stories of aristocracy should bear in mind; if you are not a mage, you are unlikely to hold power in a city that defines class by profession. The Farstriders - in game terms, the hunters - offer an alternative power base, perhaps one more morally upright, but they still do not have the upper hand. Please bear this in mind when relating your class to your character's story.
Thirdly, there are two different leaders to which a blood elf holds allegiance - Kael'thas Sunstrider, and Lor'themar Theron. They are two very different people.
Kael'thas has gone insane, and betrayed the city and the people by allying with the Burning Legion. Many players profess knowledge of this openly in Silvermoon. In the past, this did not fit; the common man now knows of Kael's betrayal since his attack on Silvermoon City and kidnapping of Mu'ru.
Lor'themar is more tricky; some say that the quest blood elf players are given to contact the Horde, in which he tells Thrall something along the lines of "what we suspected is true", shows he knows the truth about Kael. Lor'themar has become the official leader of the blood elves of Quel'Thalas with Kael'thas' betrayal.
Relation to the rest of the Horde and to the Alliance
This is a big issue that blood elf RPers make lots of mistakes with. There is one fundamental rule:
You do not automatically like the rest of the horde but it's down to you. You can trust them or not.
Remember, you are a cultured, scholarly race, and every other race in the horde is ostensibly completely unlike this. There are also ancient conflicts between some races and your own; you have been fighting trolls for centuries, for instance. While your enemies have never been Darkspears, you are unlikely to trust them, nor are you likely to be pleased to see them in your lands. However you don't call them barbarians and shout them out of Silvermoon.
Forsaken are a bit different, and a bit more open to individual preference. Some players will prefer to RP a hatred of them, as they are suffering the same affliction that killed the majority of their race and caused Silvermoon's downfall; others, like the questgivers try to reinforce, will see them as valuable allies against the Scourge, and facing a similar plight to the blood elves. It's up to your character's personality here. Plus they, while violent, have a deep scholarly past within the apothecaries.
Orcs and tauren will probably be regarded as savage and crude; they are not the traditional allies of the blood elves, and their societies, especially orcish ones, consider physical rather than mental strength to be the greatest merit. They will most likely have to earn your character's trust and approval. Tauren, however, are rather peaceful. The orcs are no longer brutal monsters they once were but have reformed under Thrall and his diplomacy.
Humans are also a mixed bag - their racism caused the Alliance to betray your people, but on the other hand you may have had some good human friends whilst in the Alliance, or perhaps in places like Dalaran. You will probably be indifferent towards dwarves and gnomes; react to them in a similar way as you react to humans. It's pretty much the same on your side but gnomes don't bear grudges often and they delve into the arcane as well.
Draenei are an uncertainty. With knowledge of Kael's adventures, you will have known they helped the blood elves and Illidan, and so you might look upon them favorably. It's difficult to say how a blood elf would react to them. Thoughts? The rivalry between the Aldor and the Scryers could be a good way for you to show your choice or make you choice on trusting them or not.
Night elves are unusual. Most night elves strongly distrust blood elves because in the past, the Highborne (now blood/high elves...and now, many of them blood elves...) caused the Sundering. Your character may choose to return the distrust or not. If you don't distrust the night elves, you are likely to be upset by them and/or even disgusted, thinking them less cultured and savage (though they are actually quite cultured and well-read, so this is ironic; the blood elves have quite the high regard for what they see as "cultured"....and it's usually their own).
Lots of people use roleplaying a high elf to bypass the necessarily angsty and perhaps undesirable features of being a blood elf. This has a few major issues.
A large amount of high elves still pledge allegiance to the Alliance. Declaring yourself as a high elf should lead to serious mistrust from other members of the Horde. Though the blood elves are biologically the same as high elves, the blood elves have green eyes whereas the high elves have blue ones. Blood elves also generally have light to dark reddish skin due to fel corruption, whereas high elves generally have peachy-pale skin tones.
Most high elves are regarded as cowardly and disrespectful by most blood elves for not honoring the fallen by changing their racial identity. You will not be very welcome in Silvermoon, therefore, and may wish to keep your identity secret and your blue eyes hidden from view. You also don't tend to take as many risks as the blood elves do in their arcane experiments.
Finally, the numbers of high elves are very small compared to the blood elves, and while they tend to be scattered around Azeroth, Dalaran holds the largest number of them, where many pledge alliance to the Kirin Tor and the Silver Covenant. Thus, roleplaying as a high elf, you would likely be a part of either faction, or you can also pledge allegiance to Stormwind. Apart from that, there are many interesting RP opportunities for a high elf. While blood elves have embraced a new way to sate their magical addiction, high elves have to withstand the numbing addiction on their own without succumbing to it, some using meditation as a way to do so.
Finally, some basic information on each class.
Death knights will likely be the most hated of all blood elves. In the Third War, the death knight Arthas Menethil tore through Quel'Thalas with the Scourge, destroying most of the land and half of Silvermoon City before tainting the Sunwell, leading to its destruction. The Dead Scar stands as a permanent reminder of this. You may not have personally defiled the Sunwell, but VERY few blood elves will trust you because of this. You're very unlikely to have friends among blood elves. The few blood elves who don't despise you will be extremely cautious when dealing with you. The other races of the Horde won't be too fond of you either, other death knights aside.
Mages are the elite, and are mostly dealt with earlier in the guide. They could well be reclusive and weary due to extensive studies. Their magical addiction could be furthered or lessened, depending on your choice. The blood elves are known for not fearing the arcane so you are likely to be bold and reckless compared to the more conservative humans and gnomes. You are generally an elite caste and sometimes consider yourself above other classes, however as mentioned in an early blood elf quest, the blood elves have to work together.
Warlocks are mages that are following a different path. Like all warlocks of all races, you may be mistrusted for this, but this is probably less likely with blood elves than other races. However the orcs have a supreme distrust of warlocks and shun them. Blood elves are known for their experiments and the warlocks are former arcanists. Perhaps your experiments into magic went too far. Destruction Warlocks, however, not using minions, can be Blood Mages.
Priests are three things - they can be either true followers of the light, dedicated to restoring hope into their people, or they are akin to shadow mages. Shadow priests, especially in shadowform, will probably be regarded with a mixture of fear and interest. Discipline priests are a more unusual type as they are somewhere in between. Their type is generally about controlling and manipulating others, similar to the warlock's succubus minion. Priests are less evil than warlocks and rogues and less reckless than mages. You would generally be the scholarly type of blood elf rather than the addicted, reckless blood elf. Some priests may have also gained their powers by the same means as most paladins, not through faith, but through the manipulation of the Light magics drained from the recently lost Naaru. These would be more akin to mages manipulating magical energies than religious leaders. They would merely be mages of a different focus.
Rogues are criminals, basically, and will be very low down in society. They will probably be jealous of the spellcasting elite, and may suffer more from their addiction than the magical classes. Remember that the blood elves are exiles which is a term very close to rogue. You don't need to focus on the criminal side, instead the exiled side. Not all rogues are criminals. You could possibly be a spy or espionage agent for the military, the needed type over the unwanted criminal type. Just don't be the cliche distrusting, hidden rogue. All blood elves must do their part and not hide from their own society. Actually, Subtlety Rogues can use shadow magic.
Paladins are a very new addition to society; some will shun you, as a either a betrayer of the light and a criminal - Priests, most likely - and some will welcome your powers with open arms. It depends on their reaction. You are likely to have a fairly twisted personality for accepting the imprisonment of a perfectly good creature, but will share the quality of wanting to protect your people with the Alliance paladins. The Blood Knights will obviously welcome you. Warlocks will likely reject you or shun you at the very least. You tend to preserve the traditions of the high elves rather than going into the addicted blood elves.
Hunters have the option of being a member of the Farstriders, who are a part of Silvermoon government, who, while not holding anywhere near the power the Magisters do, are still a power base in Silvermoon. They are much less susceptible to negative magical influence than the caster classes, as are rogues, and possibly feed their addiction from the natural magic that infuses the world. There isn't much information on that, though; it was only a memory of why hunters had mana. If someone has info, please add it. If not Farstriders, which is likely - the Farstriders are a small group - they are probably fairly outcast, perhaps even hermits, as they are remnants of when the high elves were much closer to the natural environment. The starting quests are testament to how far they've separated themselves from this. With the release of Cataclysm, Hunters will now use Focus, a similar resource to energy, as their resource for abilities instead of Mana.