The most popular games are cricket and 301/501/701. In 301 for example each players starts with 301 points, and you count backwards (for example if you hit 20 on your first dart, you then have 281)... once you get down close to 0 you have to close out exact or else you bust (for example if you have 10 points left and you hit 8 , leaving 2, you then hit a 3 on your next dart equalling 11 - this is a bust and you go back to 10, you have to hit 10 exactly - whether it be a 10 on the first dart or a combo of 10 on all 3 darts i.e. 7 then 2 then 1). You can make this game more challenging by having to double or triple out - for example you have 40 left, you HAVE to hit a double 20 to win.
The only other game I play besides cricket and 301 is "Round the Clock". All you have to do here is hit 1 through 20 in order. Once you hit 1, you move on to 2, and so on... Sometimes I play where you have to hit bull at the end to win.