There are lots of good vegan places in Eugene.  However, one of my favorite things to do is hit all the natural food stores and look at what they've got on the hot bar, etc.  If you can find some mac and "cheese" made by the Cornbread Cafe... get it.  It's amazing stuff (as is their southern fried tofu...)

Places to definitely check out:

The Divine Cupcake - awesome vegan cupcakes. 
Pizza Research Institute - a little pricey (but not too bad.)  But c'mon - vegan pizza that's so ridiculously good?  This would be tops on my list of places to visit. 
Morning Glory Cafe - Good stuff, as well.
Lotus Garden Vegetarian Restaurant - I think they're all vegan now, but you should check before going. 
Viva! Vegetarian Grill - a food cart downtown.  We don't go there much, only because there isn't a lot of stuff my kids like.  However, it's good.

If you're not from Oregon, you should also look at checking out Cafe Yumm!  It's a local chain that has amazing rice/bean bowls.  Definitely worth a shot.

Let me know if you have any other questions.