I haven't been all over the country, let alone the world so some of these places are going to be "mom and pop" restaurants that are local to my area. Some of them are going to be national chains. There is a small list of places local to my area HERE .

Ruby Tuesdays -
They had changed their veggie burger to a regular Garden Burger just when I brought my sister over there just to try this "great" new burger. This was a year or more ago.
However, my sweetie and I went back tonight (7/30/05) and I asked her about the 3 new veggie burgers that were on the menu and she told me they had gone back to the original ones!!! Yay!
Now the burgers are made Veggie Land Burgers. I've gotten better burgers out of the freezer section of the grocery store since brands like Morning Star Farms and Boca have improved so much. HOWEVER!, as far as burgers for vegetarians and vegans that eat out, I would highly recommend the original veggie burger at Ruby Tuesday's!
 

Andrea's Homestead Cafe -
This place is located conveniently on the main drag in Lyons, CO (U.S. 36).
 If you are entering town from the east and traveling west on 36, the restaurant
is on the right-hand side of the road.
I was really surprised by this place. When you walk in there are animal heads on the walls and miscellaneous "stuffed" animals. The decor is incredibly icky.
However, I was very surprised to find that there were quite a few vegetarian items on the menu!!
I had the Vegetarian Green Chili Omelet. It was just a cheese omelet served with "German" (Diced) potatoes and whole wheat toast.
I'll have to say this might be THE best breakfast I've ever had!
The omelet was temperature hot, not luke warm, the potatoes were cooked in herbs that made them very tasty and the toast was wonderfully chewy! I don't normally eat whole wheat toast but this whole meal was fabulous! The green chili wasn't spicy at all but it was very flavorful. Normally I wouldn't eat anything that didn't carry a "3" spice rating or above but with all the cheese in this omelet and the potatoes I thought I could over look the heat factor. It was a really great omelet.
If you can get around looking at the decor you can have a great vegetarian breakfast here.

Suehiro Japanese Restaurant
223 Linden St, Suite 103, Ft. Collins, CO
Ok...this is a sushi restaurant and the first thing you'll notice is it obviously smells like dead fish. If you can't stand this then you will be really unhappy with this place. (I can barely stand it myself). Also I should say that I know one of the chefs. His name is Jeff. "biker Jeff" not "oriental Jeff". :D 
I have found that they will make some great vegetarian sushi if you ask them to. However, you need to be willing to ask what's in everything they just hand you. The Miso soup has fish stock in it. They will make you a great vegetarian tempura but the dipping sauce for the tempura also has fish stock in it.
Long story short, if you're willing to ask questions and trust in what they give you, you can get some really great veggie sushi here.