Since vegans chop a lot of vegetables it seems important to talk about knives and how to choose them. I'm guessing a lot of you already know this and if so, just stop reading now. :)
First of all, don't buy a set. Second, don't buy a cheap (except maybe Forschner knives) knives. Good knives last a lifetime and are worth the investment. Even if you have to save your pennies for months to buy one knife, you should do that instead of buying cheap knives. I have Wusthof's, but Henckle's are equally good. I know some people will disagree and say that cheap knives are fine, but after years of using cheap crappy knives we got as a wedding present and then switching to nice knives, I just disagree. Cooks Illustrated also seems to really like the Forschner knives as good quality inexpensive knives.
The first knife you should buy is an 8" Chefs Knife and then if you have never used one before, watch a video about how to hold it and use it (watching my Mom with the knife I bought her about kills me). It is the one indispensible knife in your kitchen. It can do everything and is great at chopping fresh herbs and mincing garlic. If you can have 2 "chefs knives", I'd recommend a Santuko. I do almost all my chopping with my Santuko. I love it and would cry for days if something happened to it. It is not so great for fresh herbs though, so then I pull out my chefs knife. My husband Mike uses the Chefs knife almost exclusively.
You really don't need any other knives, but if you can have more knives, a good serrated knife is next in line. I have 2 serrated knives: a short tomato knife (it's good for slicing fingers too) and a very long bread knife. My tomato knife is oddly named a "sausage knife" in the Wustoff catalog.
I also have a wooden knife block to keep my knives in. Don't just throw them in a drawer, give them a safe home.
And while it is not a knife, a peeler is indispensible when prepping for dinner. A regular old oxo peeler is best. And next is the oxo serrated tomato peeler, while it is clearly just a bonus tool, it peels tomatoes and peaches easily (without boiling water).