The only reason to clean a rimfire is if accuracy is important to you. Just like any other rifle, they will become fouled with lead and carbon. This is especially important in the leade area where a lead/carbon ring builds up and it builds up rather quickly. This will not be noticed so much with run of the mill cheap .22s shooting bulk ammo, but anything with a match chamber and shooting match ammo, you will quickly notice a drop in accuracy.
Last year I won the IR50/50 Unlimited Nationals(.22 benchrest shot at 50 yards and 50 meters) and I clean my benchrest rifles and accurate sporters (Cooper 57M)after every target (roughly 40 shots with sighters). The vast majority of benchrest rimfire shooters clean after every target and those that don't will clean every couple of targets. The ones that want to win, they keep their barrels clean. Consistency is the key, and it's easy to repeat clean than some level of dirty. Rimfire barrels will lead up just like any other rifle shooting lead bullets. For shooting minute of tin can though, it's not that important.
My cleaning is done with a quality one piece .20 cal rod, bore guide, .22 pistol bronze brush, .20 jag and rimfire blend solvent. For my 10/22, I just use a boresnake. That's just for plinking.
This is what I was taught about competitive shooting with .22, and is basicly what I practice.
But like I said earlier, my hunters and plinkers are cleaned only in inclimate weather and when I'm bored to tears.
