There are two types of radar ATC (and the military uses) - primary and secondary -
a decent explanation is here.
Primary radar essentially attempts to detect anything of substance in the air - obviously their main objective is planes, but it also picks up flocks of birds and weather (thunderclouds and heavy rain for example). The reason stealth planes are made the way they are is to not get seen by primary radar.
Secondary radar just picks up airplanes' transponder codes and ATC receives information depending on what options are selected by the pilot on the transponder. Pilots can choose what information does and doesn't go out (they can disable altitude readouts for example). Stealth planes don't have to dodge secondary radar because they (hopefully) have their transponder off.
As some mentioned, you could "piggyback" on another aircraft by just turning your transponder off and the radar will pick up your two planes as one. Of course occasionally they may show up as 2 targets, but if they're quite far away they are from the radar tower chances are it comes up as one. You see it with military formations all the time. With a large plane it is less likely of course, but still possible. Additionally, if you're flying below a particular altitude radar might not even pick you up.
You would be surprised at how much stuff radar could possibly miss, and how much actually goes on in the air. There are weapons controllers covering the entire US (and Canada - good ol' NORAD) that deal with Russian and other 'bogey' aircraft all the time. Obviously you just don't hear about it...