They are reliable in stock form, and light on the wallet.
Accuracy wise, they are okay...the cheaper marlin mod. 60 has proven more accurate stock, than any stock 10/22 i've ever played with...
I big key to their popularity is both brand name, and aftermarket accessories.
Because they are so simple modify, they are a popular platform for modications. Just about every barrel maker out there sells a 10/22 barrel, or more...between sporter, heavy, fluted, helical flutes, aluminum, stainless, carbon fiber, etc... Barrels take but only a few minutes to interchange.
There are a hundred different stocks available, from mild to wild...so you can express yourself easily...lots of trigger components, and bolt modifications are available as well.
And lets not forget how CHEAP .22lr's are to feed!
Our local range is split into a large bore and smallbore/rimfire range...there's always someone with a custom 10/22 shooting in the rimfire range... Some of the more serious shooters are putting 10 shots in one hole at 25yds, that doesn't measure any larger than than a hole where only ONE bullet has passed. I've seen groups in the MOA range at 100yds as well, with match ammo.
You can get a lot of money invested into these things customizing them...but you can turn them from mild shooters to wild paper punchers quite easily.
They're also popular in area's where squirrel hunting is a big time sport...