Drink

Amsterdam's famously wild nightlife caters to all tastes and budgets.

Bars and pubs

The archetypical Amsterdam watering hole is the bruine ("brown bar" or "brown café"), a neighborhood pub of sorts with gorgeous dark wood panelling - hence the name - and booths. These do not sell cannabis, see coffeeshops below for that. Popular entertainment areas with lots of bars are the Leidseplein and Rembrandtplein.

Clubs

Amsterdam features many famous clubs, including:

AIR Amstelstraat 16 (near Rembrandtplein)
Bitterzoet Spuistraat 2. This placed used to be alternative, but changed ownership and is now more hip hop and R&B oriented. Check their agenda to see what they're doing.
Club HOME Wagenstraat 7 (near Rembrandtplein, at the old Sinners in heaven location)
Club 8, Admiraal de Ruijterweg in West. A large alternative place with lots of art on its walls. There's ping pong, a very local and fairly young crowd.
Escape Rembrandtplein 11, a large, fairly uninspiring club that plays mostly mainstream house music.
FlexBar Pazzanistraat 1 (in the Westerpark), a small venue off the beaten path in Westerpark that plays electronic music, often until 5am.
Jimmy Woo Korte Leidsedwarsstraat 18 (near Leidseplein) is an upscale, relatively small club with table service and a notorious door policy. Boys, don't come alone.
Korsakoff Lijnbaansgracht 161 (near Leidseplein) A more alternative, run-down but cheap place that often has live music.
Melkweg Lijnbaansgracht 234 (near Leidseplein) can be compared to Paradiso, although its live venues and events can eat up some of the nights. Check their listing.
Odessa Veemkade 259
Panama Oostelijke Handelskade 4, quite far away but can have its nice nights and the view on the water is excellent.
Paradiso Weteringschans 6 (near Leidseplein). Somewhat the safest bet in town. It's impressive, walks a fine line between pop and alternative, gets a mixed crowd and isn't too crazy expensive. It popularity is obvious by the huge line on the weekends.
Studio 80 Rembrandtplein 17 Is an somewhat more underground, intimate club that's easy to miss because of its flashy neighbours. It prides itself by trying to stay on the forefront of electronic music in the city.
Sugar Factory Lijnbaansgracht 238 (near Leidseplein)
The Power Zone Daniel Goedkoopstraat 1 3 (metro to Spaklerweg)
Tonight club (in Hotel Arena) 's Gravesandestraat 51
Trouw is club that opened in 2009 in an old newspaper building with the same name. Far away, amazing space, and great music. Can be a little expensive because of its cool.

Coffeeshops

Amsterdam is renowned for its liberal drug policy. Coffeeshops, not to be confused with coffeehouses or cafes, are allowed to sell cannabis and hash for personal use (not more than 5 grams). While technically still illegal, mostly to comply to international treaties, personal use of (soft) drugs are regulated by the Ministry of Justice under an official policy of gedogen; literally this means to accept or tolerate, legally it is a doctrine of non-prosecution on the basis that action taken would be so highly irregular as to constitute selective prosecution. The city council of Amsterdam only allows coffeeshops to operate with the provision of set, non-transferable licenses - as shown by an official green and white sticker on the window of a coffeeshop. Coffeeshops are only to sell soft drugs (e.g. cannabis), selling of other drugs is not allowed. Also selling of dried halugenic mushrooms is not allowed.
That said, drug usage is increasingly being strictly controlled by the Dutch government. Garish advertising is not allowed (look for red-yellow-green rasta colors and the English word "coffeeshop"); no alcohol or edible cannabis products may be sold inside a coffeeshop; customers who want to smoke their weed mixed with tobacco are limited to special sealed 'smoking areas'; the amount of coffeeshops has decreased significantly since 1995; coffeeshops within a '250 meter school zone' have been closed down; and the usage of magic mushrooms has been forbidden since December 2008 (after two fatal incidents with foreign tourists).
Still there are about 250 coffeeshops in Amsterdam, most of them in the Old Center. Prices hover around ?7.50 for 1 gram, with the average joint holding around 0.33g and a 5g/person sales limit. Most coffeeshops are happy to recommend varieties and prepare your joint for you. Some offer vaporizers/inhalators for people who don't want to smoke.
Using (soft)drugs is not allowed in public places, though in reality it will never be an issue. Just stay away from children's playgrounds and schools. Many coffeeshops offer a 'smoking lounge' where softdrugs may be used. Also note that smoking cannabis is regulated under the non-smoking act, meaning that it is only allowed in a closed area where no personnel is working.
Bulldog. Chain of touristy coffeeshops.
Grey Area.
The Bluebird - one of the best selections of pot in Amsterdam.
De Kuil (420 Cafe)
Global Chillage - Good produce and nice tunes but uncomfortable seating.
Barney's. Multiple Cannabis Cup winner.
Rokerij. Four coffeeshops.
Kadinsky
Hill Street Blues - lively atmosphere but buy cannabis elsewhere.
Club Media - Completely organic menu, fair selection, good prices, lovely staff, free fruit!
Katsu - Just around the corner from Media, good prices + nice atmosphere.
The Greenhouse - usually pretty crowded but when warm or if you can get a seat definitely one of the nice coffeeshops near the red light. Also has a bar next door.
De Dampkring - three locations, bought out Pink Floyd and renovated it. Original shop featured in a scene in Ocean's 12.
De Kroon.
Abraxas.
Homegrown Fantasy.