The best list of vegetarian restaurants in Bangkok seems to be at http://www.happycow.net/asia/thailand/bangkok/ (Thanks Joel)
My favorite restaurant in Bangkok is Beruit, on Silom in the J-City mall right near the Silom BTS exit across the street from Central. It is in an open mall that also has Subway (good veggie footlongs) and KFC (meat eaters only).
Beside Beruit is a new Tex-Mex food stall that makes enjoyable, non-oily burritos, tacos and nachos.
The place I'm most likely to take a date is Crepes and Co on Sukhumvit soi 12, which has an extensive menu of vegetarian (and meaty) Mediterranian food.
I would recommend avoiding the neighboring Cabbages and Condoms. Great social mission, lousy veggie food.
Speaking of Crepes, the monomaniacally crepe themed Bug and Bee on Silom down the street from Beruit has an extensive and rotating selection of vegetarian food, and is a fun place to chill out. For some reason, it is a place I would only go if I was in the area and felt like hanging out, even though the food is pretty good. Strangely, every single dish seems to have crepes or crepe components (ie noodles made from crepes) in it.
The food courts in the malls are excellent options. The best is at MBK, which has a vegetarian section with mock meat, as well as an Indian and Lebanese stall. You can also get mango and durian with sticky rice. There is a second, more upscale food court at MBK that reputedly has a branch of the Tamirand Cafe. The food court in the 1st floor food hall at Chitlom central has many options, including barley salads, vegetarian Thai food and Mexican. The sixth floor food court in the same mall is swanky: you could bring a date there for dinner. It has international food of all types. The international food court on the 6th floor on Emporium is similar. There is a hidden Thai food court nearby where you can get pasta with tomato sauce. Otherwise, veggie pickings are slim (but cheap and tasty).
The main Tamarind cafe, a pure vegetarian restaurant on 27 Sukhumvit Soi 20, has a nice atmosphere, incorporating a lush rooftop garden and cool photo gallery. It is a comforatable place to read a book and chill out. But I don't go too often because it is a little bit too expensive and not quite tasty enough.
Govinda on Soi 22 offers Italian vegetarian food. You have to go down a small sub-street about 200 meters down from Sukhumvit. It is more reasonably priced and the food is more tasty than Tamarind. There is a Scandanavian hostel and bar beside it that is a cool place to play shuffleboard and relax.
Lemongrass on Soi 24 can make excellent vegetarian Thai salads, although they are not on the menu. It has really good Thai food and is a great place to take visiting relatives.
Komala's Indian fast food restaurant on 15 Sukhumvit soi 20 is excellent and cheap, but the ambiance is like a McDonalds.
For street food, a sidewalk place on Sukhumvit right beside Thong Lo has a picture menu and some great veggie options. Try the "Dok Kra Jeaw."
Around Thong Lo, Woodstock has a great bar atmosphere, a good pool table, and some nice veggie options, including a black bean chili. Soi 13, Sukhumvit Soi Thonglor.
If you want to spash out, Harvey (129 Sukhumvit 55, Thonglor Soi 9) has a relatively affordable 500 baht fixed lunch, which usually has a vegetarian friendly option.
Places that friends have recommended and I have been meaning to try are a Thai vegetarian food court at or near the Chattachuk market (more information welcome!) and Anotai at 976/17 Soi Rama 9 Hospital, Hwaykwang (at Bangkapi).
Untested recommendations from friends:
whole earth Sukhumvit soi 24-26
Ob-oon, Chinese-style vegetarian on Rama 4 in the Samyan area
PLEASE TELL ME YOUR EXPERIENCES AND PICKS