After years of playing roundwound strings, I got tired of that metal 'zing' that comes with rounds. I switched to tapewound strings amidst cries of 'deadness' from other players (mostly guitar players). My Jazz bass wouldn't ground noise out through the strings so I swapped them out for some taperwound nickel rounds - which were great, but had too much sustain for my liking. After some consideration, I decided to swap out to a set of Flatwound strings (D'Addario Chromes) and was immediately confronted with 'deadness' (and not the typical Phil Lesh vibe I want to associate with that made up word). I've recently gone back to Tapes - this time D'Addario tapewounds - and I'm so happy that I did. No more metal 'zing' confusing my notes for something they're not, and I get great treble tone coming from my bass all the same...just not as much.
Very few players try tapewound strings because they think that it will kill their tone. I think it sounds more natural - more 'acoustic' (like a wood bass) to me and I get a great feel out of the notes that I play. My amp turns up and I can run my gear to get as much note definition as I'd like. Instead of a smiley EQ (turn up the bass and treble), I scoop out some lows, turn my volume up, and adjust my mids to taste.
If you've got the extra cash to play a set of strings and not like them, I would suggest that you try Tapewound strings. They can work for every genre (well, maybe not metal) if you're running your gear properly.
Save that, if you're going to stick with rounds, a lot of guys like Rotosound and DR (but the same goes for a lot of other makers as well). I've read some great things about D'Addario FlexSteels and if you want to try different gauges it's hard to beat Ernie Ball Slinkies for price. (maybe no-name strings like NoFame?)
Also, if you want to try a 'balanced' set of strings, the guys (and girls? I have no idea) at CircleK have impressed a lot of players with matched even tension sets.
There's a lot to try, a lot to buy, and until you find something you really like you'll never quite know.
