The beer isn't smoked, but some of the malt is. The classic example is German rauchbier, which uses up to 100% smoked malt. Smoked porters are another common smoked beer - these tend to use 10-30% smoked malt (rough guess).
There are various smoked malts you can get - the most traditional is German rauchmalt, which is smoked with beech wood. As mentioned above you cam also find cherry smoked malt. There is also peat smoked malt, but this is very powerful stuff and should be used judiciously, if at all (many brewers will tell you peat smoked malt has no role in beer making)