You can get rosin off strings completely (and not abrade the strings) with a copper scouring pad -- sold at many large grocery stores for less than a buck.
I used to use metal scouring pads or steel wool, but they will abrade the metal on the strings, and you don't want that.
That's what I use. They are very cheap, and they make my strings seem like new.
There's also rubbing alcohol, if you are careful not to get it on your finish. The copper is definitely what I prefer, though.