I’m here under my real name. It hasn’t caused me any problems yet. I also use my real city in the Location bar to keep people from stalking me and ending up with either a Detroit Unitarian Minister or my same-state-but-not-same-city father, both of whom share my name.
So far, I’ve never been stalked or prank called. (Note: not a request.) Some combination of being lucky, being boring, and most people I deal with being sane.
I’d rather people not be able to find me without my permission. With my last name and city (which I mention often enough in posts), anybody can find me.
A few months ago, a guest started posting odd hypotheses about history and the nature of the sun. At first I, assuming he had simply failed to do research or use critical thinking, laughed at him. Then it became clear this man was mentally ill and I tried reaching out to him. He was quickly convinced that I could help him. However, this was not because he believed I could treat him or bring him to a good psychiatrist. He believed I was some sort of enlightened prophet sent by G-d. A month or so later, I mentioned a store in my livejournal. It was the only time I’d given an address for any place I’d described. The man was convinced he had to go this store, despite the fact he lived several time zones away and had no car. I’m certain that if I used my real name, he’d show up on my doorstep.
It could happen to you too.
I used to sign my posts with my real name, but some people around here got pissy about it. So I stopped.
my user name is the genuine, honest, real-life name …of my cat.
Works fine for both of us 
I use my real name. Of course, it’s also quite a few other people’s real name. I am Steve Wright, but it’s very unlikely that I’m any Steve Wright you might have heard of …
Hey Steve, where’s that ten bucks you owe me, ya bastard?
Yes.
My ID on SDMB is based on my location (Japan), but sometimes people think I am Japanese (which I am not). My real first name can be found on my Disney fan site: http://www.jtcent.com (sorry, shameless plug).
I wish this was my real name =(
I use my real name here.
Obviously I don’t use my real name. I like the privacy, even if it’s mostly illusory, and don’t care to have the real me be an issue in board conversations. Some people don’t have a problem with writing private things on post cards, other people like to use envelopes. To me, the handle is like an envelope. You’ve got to put in at least a little effort to violate my privacy, I’m not just going to leave it hanging out there for everybody.
In the old days, net communications were more like a village than a metropolis. The people you were in contact with were part of a relatively privileged and limited group, and you’d probably know most people in RL anyway, so using a handle was a pretty transparent dodge. Besides which, some groups wouldn’t take just anyone. Quite a few took invitations to be able to join. Modern message boards are a lot more open than even some USENET groups used to be.
The thing you have to remember is that this medium is different from just about anything else we’ve had before. Internet posts are more like a public broadcast than a private communication. People who want to be famous (or infamous) or who are experts in an area rarely have a problem with attaching their name to something, no matter how public it is. Others might not want their name on every single thing they post.
Leaving aside problems with internet stalking, even nominal anonymity has a positive affect on some conversation. How many people do you think would be willing to contribute in TMI or sex threads if we all posted under real names? Only the extroverts, those who don’t mind you doing a search to see if you can find pictures to associate with the “guy who jerked off in his fish tank” or the “girl who has orgasms when she gives blowjobs”. Using real user names would probably cut down on trolling, but it might not eliminate it completely, and I don’t think it would be worth giving up privacy for.
You also might be willing to discount input from someone because their public persona doesn’t carry any weight. A guy might be nothing more than a 7-Eleven employee, but be well-respected for contributions in an area of interest. Someone who is [insert ethnicity/sex/orientation here] can talk without that being an issue unless it is volunteered. On a board, your name carries only the reputation you build with it. There are no preconceptions about the real you weighing it down. I think that being public would have a quelling effect on some topics of interest and would be an overall negative.
I sometimes sign posts with my first name, mainly to remind anyone that reads it that I’m female, as my user name is nondescript. I don’t use my last name because when I started posting I was 16 and that didn’t seem like a good idea at the time. My names, while neither are spelled the common way, are by any means unique, so anyone trying to google it would have a little trouble, not to mention if something that an employer found on line prevented me from getting a job, I’m really not sure that I’d want to work there.
I use a username that is inextricably linked to my real name. I’ve been using it a long time, and a search reveals me instantly. I’ve considered changing my username to my real name simply so people will stop misspelling it. 
I actually had a usenet stalker a few years back who called my workplace repeatedly and said he was going to rape and murder me. Unpleasant, to be sure, but I my chances of that happening are probably greater from people who live in my own state than some wacko stranger in Florida.
Wasson, are you related to the actor Craig Wasson? I like his work very much.