Are there any airlines that offer WLAN?

Definitely! Although frustratingly for me, the only flight I've been on with it, they informed us it wasn't available over the ocean (and I was flying from Hawaii...).

However, if you look at Wikipedia you can see a bit of information about it. In the US alone, there are 16 airlines with wifi onboard, and Delta alone has over 500 aircraft with inflight wifi. Free - not usually, but definitely available.

Gogo Inflight Internet is the most common provider in these cases, and indeed their wiki page has a list of airlines in the US offering. To quote:

Gogo service began on American Airlines in July 2008. The first routes served were JFK to San Francisco, JFK to LAX, and JFK to Miami. They are currently expanding to include Gogo service on the full American Airlines domestic fleet.

On August 5, 2008, Delta Air Lines announced it would install Gogo on all its domestic aircraft, which has since been completed. Recently, Delta announced that Gogo service would be expanded to include its full fleet of Delta regional jets. but a 2009 merger with Northwest Airlines added to the fleet. By early April 2010, 437 of 540 aircraft in the combined domestic fleet offered Wi-Fi, with remaining installations expected by summer 2010.

Virgin America became the first airline with fleetwide in-flight Internet access, in March 2009.

On July 14, 2009, AirTran Airways completed installation of Gogo on 136 of its aircraft.

October 2, 2009 saw the launch of Gogo on United Airlines' p.s. flight 23 from New York to Los Angeles. The company plans to have Gogo installed on its entire p.s. fleet by November 6, 2009.

On November 20, 2009 Gogo announced that Air Canada has begun trials of the Gogo system on select Toronto-Los Angeles and Montreal-Los Angeles flights which occur in large part over the continental US.

On February 24, 2010, Alaska Airlines announced that it will offer Gogo on its full fleet. The full fleet installation was completed in the fall of 2011.

On March 29, 2010, US Airways announced that all its Airbus A321 fleet would offer Gogo by June 1, 2011. The full fleet installation was completed in the fall of 2011.

On February 5, 2012 Frontier Airlines announced that it had equipped all of its Embraer E190 aircraft with Gogo to begin service on February 6, 2012.

Lufthansa has WLAN in its long-haul aircrafts (A330, A340, A380 and Boeing 747). The thing is called FlyNet. This service is available in the skies of Europe, the North Atlantic and North America. Of course, you can do gaming, but at a rate of 10.95 EUR per hour you must be quite addicted to your games ;-). You can also redeem Miles for WLAN access.