So today I decided to see if I could come up with several death knight "template" characters, which could serve as inspiration for roleplayers already thinking about their own approach to this problem. Feel free to leave your own template characters in a comment, or to create template characters of other races and classes as well, if you desire.
One rule I'm trying to stick to here is that all these characters are basically good. They became death knights without truly becoming evil, or if they originally joined the Scourge with evil intent, they have some plausible reason why they would later on turn against it. In some cases, the character might not be "good" so much as "opposed to the evil guys bent on destroying all life," for some reason. Also, in some cases, I'm trying to go for a very light-hearted, humorous, or even innocent approach to the character, in so much as that is possible with a death knight.
You were once some sort of warrior fighting the scourge, but like Sylvanas and Highlord Mograine, Arthas defeated you and decided to raise you from the dead to serve him afterwards. For a long time, you have longed to be freed of this slavery and corruption, and now, with the help of other death knights who are breaking free of Arthas' control, you too are gaining your freedom. Now, you are trying to pick up the pieces of your broken life, gathering what you have left to form something new, some shred of hope to cling to.
This fits best with forsaken characters, who are obviously undead, but if you can choose some sort of pale skin color and make another race look mostly dead, then it could work with them too. Don't try to pull this off with your typical ruddy blond hero -- death knights certainly aren't all undead, but this one is, and if you aren't going to be forsaken, then you'll need to find another way to make him look the part. Also, be aware that this type of story has been done lots of times before, so you should try to make yours unique in some way, without being melodramatic. Perhaps, if you died in a particularly embarrassing or ironic way, for instance, your character could play off lots of cliches in the horror genre and also make other people laugh without being a total farce.
You were just a youth at the time the Scourge came through and destroyed your hometown. At the time you joined the Scourge out of fear, thinking it was your only way to survive, but all along you planned to leave it if the chance came. You found others like you, and together nurtured one another's courage until the time to strike finally arrives.
This could work for humans, orcs, or blood elves, all of whom could have suffered at the hands of the Scourge during the Third War. Humans and elves in and around Lordaeron obviously got invaded by the Scourge, and there were orcs in concentration camps around that area as well. Dwarves (and maybe gnomes too) could have conceivably been caught in Muradin's lost expedition or something, with somewhat similar results. Trolls, tauren, night elves, forsaken and of course draenei would not have been in the right time and place for this story to make sense for them, however.
You come from a culture that loves nature and life, but for a long time you were tempted to know what this corrupt death magic is all about. The more your people warned you against it, the more you wanted to know until you finally set out for Northrend to just have a look. Needless to say, you were intrigued and took up your studies with enthusiasm, only to be horrified at the depth of corruption being a death knight involved. Now, breaking free of the Scourge, you know it is too late to go back to your own people and ask for forgiveness, but you hope that by your example, you can prevent others from following your path.
This story could work well for tauren and night elves. It could also be called "recovering drug addict," and it's different from "celebrity in rehab" mostly because the character doesn't have any pretensions of being cool or unique. He or she just wanted to know a lot of things that shouldn't be known, and now wishes to make good of this mistake.
You used to go digging up graves, trying to assemble various body parts together and zapping them with electricity, but nothing ever seemed to work, no matter how loudly you shouted "It's alive!" Being a loner type, you didn't have many friends to talk you out of dumb ideas, so you decided to go and find out what really made life work by learning about undeath straight from the Lich King himself. Now that you've become a death knight and all, you've realized that Arthas is a nasty sort and you don't want his kind running things, but you're still convinced that if you could just get those assorted limbs, brains, and intestines arranged in the right way and infused with the right quantity of mystical energies, you could create not some ghastly monster, but a real living creature, albeit a rather ugly one.
This idea is tailor fit to gnomes, but it could work for a number of other races as well, since all races are capable of becoming engineers, and anyone can be bitten with the lust for scientific advancement. This character could be a serious commentary on philosophical issues like the original Frankenstein was, but it seems more fun to fill him up with fun references more in the vein of Young Frankenstein. Any horde race other than blood elves could even get away with calling themselves "Igor," "Igorina," or some variation thereof.
While most religions in WoW, such as the Holy Light, Shamanism, and worship of Elune (Elunism?), are focused on reaching some sort of enlightenment through virtues, good deeds and the like, there could be a subset of mystics who seek spiritual enlightenment through direct, face-to-face confrontation with the grotesque realities of life, just like real life people who sometimes undertake tantric rituals. Some, such as blood elves, may see this as the key to freeing themselves from an existing problem or addition, even though it goes in the face of everything their people stands for.
This concept suits blood elves most of all, but I could see it made to fit any race except gnomes (who tend not to be all that religious in their worldview).
That's a review of the best ideas I came up with. Can you think up some more? I'd be especially interested in plausible death knights that were either humorous or innocent or both.