The most famous Liechtensteiner is probably the Olympic Gold medalist downhill skier, Hanni Wenzel. If the US had been anywhere close to a medal, we probably would have got some stupid lawyer to to sue on the grounds that she was probably Swiss, and they were cheating so they could sneak in another gold medal shot.
Luckily, there is more than false teeth and corporate swindlers to Liechtenstein. They have their priorities straight, at least partially.
The soccer tradition in Liechtenstein is surprisingly well developed, with several clubs available to check out. You can also get some in-depth coverage of Liechtenstein's campaign to qualify for the 2002 World Cup in Charlie Connely's excellent book, Stamping Grounds
Despite having a population about half the size of a Borussia Dortmund crowd, Liechtenstein has a well developed soccer tradition since the 1930s. The national squad has competed in major FIFA and UEFA tournaments, although their successes are rather limited to not getting slaughtered. However, in 2004, they achieved some positive results: In the World Cup qualifier, they trailed 0-2 to powerful Portugal and came back to tie 2-2. Then they continued their great run, winning 4-0 away to Luxembourg. Meanwhile, the Portuguese were so embarassed, they thrashed Russia 7-1 in their next outing...
Most of the decent Liechtensteiners play in the Swiss leagues, although the best player has made it a bit further: striker Mario Frick played with Hellas Verona in the Italian Serie A 2001/02, played for various Serie B sides and was back with Serie A side Siena in 2006.
Getting there is relatively easy. From the Austrian side, take the train to Feldkirch, the major metropolis of Vorarlberg state. From there, the bus to Vaduz leaves from the train station. There is a similar arrangement from Sargans on the Swiss size. I suppose you could also jump out of the window of the train at Schaan and walk the distance to Vaduz.