Venice Wine Bar
My favorites are Alla Botte near Campo San Bartolomeo in San Marco, Al Prosecco in Campo San Giacomo dell Orio (Santa Croce) and La Cantina on the Strada Nova, in Campo San Felice (Cannaregio.) I don't know when you are going, but I believe La Cantina is closed for renovations at the moment. Should reopen soon.
Vino Vino, already mentioned, is also a great place. I also like Un Mondo di Vino on Salizadda San Canciano (Cannaregio) and Vinus Venezia, down a calle from the Crosera in Dorsoduro. Find the Tonolo bakery, look across, and go under the sottoportego by the internet place. Vinus Venezia is down there, across from the Trattoria San Pantalon.
You'll find no shortage of places to drink wine in Venice!
Definitely second La Cantina, Al Prosecco, Vinus Venezia. Haven't tried the others Shannon mentioned except Vino Vino which didn't wow me... but I would return if in the area. Also love Do Mori and Bar La Marca which are both by the Pescheria Rialto. BancoGiro has great bottles if they have them in stock and good snacks. In nice wether you can sit at rickety tables overlooking the Grand Canal.
Vino Vino was closed for renovations when we were there in April. I second Al Marca (for hanging out at sunset--1.8 euro spritz!) Al Prosecco (for a relaxed lunch or afternoon hangout) and Do Mori (for a drink and to soak up the history).
For the wines we loved Ai Artisti; for the lively scene and cicchetti, Gia Schiavi (both in Dorsoduro). And be sure to get a slice and some beer or spritzes on Campo Santa Margherita late at night...
bar reviews after my restaurant reviews here:
Vino, Vino is located not far from the Fenice Theater. It has an excellent wine list and shares a kitchen with a high-end restaurant (Antica Trattoria?). They serve a limited, reasonably-priced menu at lunch and dinner. I am not sure what food they have available at other times of the day. It does stay open till late in the evening (at least it used to).
Also, be sure to do a "Search this board" search for 'Venice Win Bar'. You should be able to access a good number of prior posts with helpful suggestions.