Many Bernese will tell you that nightlife in Berne is not exactly what you might call spectacular, but they're probably comparing it to Zurich or Paris. There are quite a few good spots to hang out at.
For a drink or two, there's a wide choice of bars all over town. However, you might be disappointed with most central options as they tend to be annoyingly conventional, though there are an ample number of exceptions:
Du Nord, Lorrainestrasse 2 (just across Lorraine Bridge from the city center), ? +41 (0)31 332 23 38. 
Café Cairo. Another nice choice in the same area as Du Nord. 
Kornhaus Café, Kornhausplatz 18, ? +41 (0)31 327 72 70. Posh but nice and near the center. 
Kornhausbar. Located in the basement, one floor over the restaurant. It serves the best drinks in Berne, but is always crowded with overdressed people. 
Cuba, Kornhausplatz 14, ? +41 (0)31 311 64 86. with Latin-influenced Cuba Bar next door 
Most of the towns cooler bars are located around the main clubbing venues though. In the ancient Matte neighborhood, which is well worth a daytime visit too, you'll find nightlife options for almost every taste.
Dampfzentrale, Marzilistrasse 47, ? +41 (0)31 310 05 40. In this former electricity facility you'll find an excellent restaurant and bar, along with lots of cultural pearls. They specialize in urban, jazzy, electronic music and dance performances. Definitely a gem! 
PROGR_center for cultural production, Waisenhausplatz 30/ Speichergasse 4, ? +41 (0)31 318 82 70. Close to the Reithalle and even closer to the city center, you will find the PROGR. More than 100 artists, dancers, actors and musician have their studios here. It's large courtyard with the CaféBar Turnhalle is a real oasis. From September to June, they offer a cultural program with exhibitions of experimental and contemporary art, theater, performance, lectures and regular concerts on Sunday nights (jazz- connected, world women voices). 
Reitschule, Neubrückstrasse 8, ? +41 (0)31 306 69 69. Next to the central train station is Berne's most important center for alternative culture. The huge brick building is visible from far, easy to recognize by its abundant graffiti art on the façade and roof. Reitschule has the status of an autonomous cultural center, which means in firm language that it's a no-police zone. This of course gives it a bit of an anarchist touch, a touch of "anything goes". And indeed, anything does go: Reitschule features a theater, a cinema, a women's room and two concert/dancing venues, all dedicated entirely to alternative culture. Recent concerts included rjd2, Metalheadz or DJ Babu. The center as a whole is a unique experience and a must-see for anyone who has an interest in contemporary urban culture. 
Silo Bar, Mühlenplatz 11, ? +41 (0)31 311 54 12. Also in the Matte, this is a popular student hangout and disco. Admission is free and the place gets really packed on weekend nights. A nice place if you don't mind the sound (a mix of mainstream hits). 
Wasserwerk Club. This is one of Berne's traditional clubbing and concert venues for urban music. It actually features two parts: Sportwerk The very welcoming, smaller "Sportwerk", which is open all week and free of charge, offers drinks, music, pool, snooker, darts, table soccer and flipper games as well as sport events on TV in a laid back, greenish atmosphere. The bigger part of the club, the actual "Wasserwerk" is open on weekends and features excellent djs and live concerts.