Okay, randomly agreeing with many people. I went veggie when I started college, and I've never gone back. My wife and I were both veggie before we met, so we never had to deal with it from the "Oops, how do I?" standpoint.
People have already given a lot of great advice. Here's my attempt to offer a few personal insights:
1) You can find a decent substitute for just about any kind of meat. It won't be the same, but it will be something. There are a zillion different fake-burgers. We have fake hot dogs (the spicy kind, which I think even my carnivore dad liked better than real ones) when tailgating before football games. We eat veggie buffalo wings while watching football on TV. (Um, hi, my wife likes football a lot, so who am I to complain?)
2) Protein is usually not a problem. You can get it from beans and pasta, and if you're not a vegan, you can get it from eggs. My wife and I do a mix of pasta, eggs, and Jamba Juices with Protein Boost throughout the week. (Mmmm, smoooooothies) Red beans and brown rice is kind of a classic white-trash vegetarian complete protein deal.
3) What is important is that you don't do what I did when I went veggie, which is to take away meat and not change anything else. I ate salads and bread for about a year and a half, and then, when I came home one Christmas, my mom said that I looked gray. Turned out I'd not gotten enough iron. Make sure to add foods with iron in them to help out on that front, unless you like being tired and dizzy all the time.
The darker green the food, generally speaking, the more iron it has. Cooking in an iron skillet puts a lot more iron into the food, which is also good. Do not drink black tea during or immediately after food -- it does a neat chemical reaction that causes it to bind with the iron, which means that you don't get very much iron absorbed into your body, regardless of how much spinach and broccoli you just ate.
4) Take a multivitamin supplement. It's easier than trying to remember to eat some root you've never heard of in order to get some vitamin that only appears in meat and that weird root. Centrum or something like that is fine.
5) If you do go vegetarian, be clear on your reasons, and develop a game-plan. Figure out your ettiquette, so that you don't get all awkward when someone suggests that you just pick the pieces of meat off the pizza.
For example, I don't buy cheese made from animal rennet. However, at a restaurant, when there's a good chance that the only vegetarian option is some pasta covered with Parmesan cheese (which almost always contains animal rennet), I turn a blind eye rather than be obnoxious. I will, however, ask if the soup is made from animal stock, and if it is, I'll just have a salad instead. At barbecues, I ask that my veggie burger or kabob not be touching the meat stuff (or, like, right next to it where the juicy meat spatter will get onto it), but I understand that not everyone cleans their grill between each use -- I compromise by assuming that any meat products that were left on the grill beforehand have likely been charred away to nothing, so putting a veggie burger on a spot that had meat on it awhile ago is alright.
6) Finally, if you do go veggie, and you stay that way for longer than a month or so, don't just try to wade back into the meat. After a month (I think) or so, your body stops producing the enzymes that break down meat, which means that if you "break" your veggie fast by having a bigass bacon-double-cheeseburger, you are going to have some really fascinating digestive issues for the next day or so. I've accidentally eaten meat twice, I think -- and both times, I spent a lot of time in the bathroom for the next day.
Summary: It's do-able, and if you're willing to compromise on some stuff, you can do it and still be social and still go to restaurants and such. It's a lot easier in some areas than in others -- I live in Bay Area California, and when I went to my father-in-law's sun-dance in Oklahoma, my wife and I had the "Okay, whatever doesn't have meat in it" approach to life. Turned out that there was a Bennigans that had veggieburgers, and they even took the bacon bits off the salad for us. Very nice and very polite, although they probably thought we were a bit weird for our vegetarianism. If you show that you are not making an issue of it, it will rarely become an issue for others. The only person who consistently bugs me about it is my one idiot uncle, who seems very threatened by the fact that I don't eat meat. (Kahuna Burger made a good point in this regard.) I resign myself to getting one lame comment about it per family get-together, and I deal.