Well I've tried a few different heads in my time on the snare to try and get differet sounds and response. I have never been attracted to the ringing sound so much, and have always tried to dampen the ring a bit so have resorted to taping, using hydraulic heads at one point, (moon gel is a God send if you want to dampen without big bulky tape and other apparatus).
I tried Kevlar heads made by Bear, ugh-- you can play on it even if you wear a hole through it--seriously I've done it, but they ring like crazy.
So here are the heads I like best currently:
Evans EC Reversed Dot Coated Snare Batter Head--my favorite batter side or the
Evans Genera HD Dry Snare Batter Drumhead-a decent batter side and on the bottom I'm using
Evans Hazy 300 Snare Side.
I like some
Aquarian heads I tried out the
Aquarian Focus-X Snare Drumhead and like them but prefer the
Evans heads...
Remo heads are still popular though, its a matter of preference