You can run wraparound (SKS, eg.) fenders on a frame that doesn't have eyelets by using rubberized C-clamps (from any hardware store). you'll need larger ones for your fork if it has a significantly higher diameter than your seatstays.
If you have a bike with rear-facing dropouts, you should either leave lots of slack in the rear fender (to allow for wheel removal) or cut the rear fender in half to allow for wheel removal. If you choose to do the latter, throw a back-scratcher fender on top of the other fender.
Of course, if you ride where it snows, your fenders will pack with ice and cover you with sluch no matter what (hello Chicago).