They won't fall off unless you abuse them. Normal use where you don't move your computer will not cause this to happen. Most Athlon coolers use clips, but recently AMD has made it mandatory for them to use clunky mechanisms that attach to the entire socket at multiple points for very a very stable contact. Not all coolers have complied with these standards and some probably won't.
I recommend the Zalman CNPS 6000-Cu copper Athlon cooler. You can buy it <A HREF="http://www.newegg.com/app/viewproduct.asp?description=35-118-101" target="_new">here</A> for cheap. It has a nice design that isolates fan vibrations by suspending the CPU fan over a flower heatsink (for improved surface area and improved heat dissipation). It's really great and is quieter than just about any cooler out there.
My only warning about this cooler is that the fan isn't the highest quality, and it's sleeve bearing. It may start making ratcheting noises early on. If the noises bother you (they don't bother most people) then you should plan on replacing the included fan with a 92mm Papst fan and getting some rubber grommets:
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