Network performance is definitely extremely important for game servers, however this is probably an over-simplified way to look at it.
For example, if you asked the average gamer, you'd hear Internap, Mzima, and nLayer a lot as good NSP's as Jason stated. I've generally heard Cogent, Savvis, PCCW, Global Crossing as the most frequently named "bad" providers (although I'm not aware of any major NSP that I haven't seen a gamer try to flame at one time or another
). Where that gets interesting - Internap, Mzima, and nLayer are all much smaller Tier 2's that actually buy their bandwidth from the much bigger Tier 1's which INCLUDE Cogent, Savvis, and Global Crossing.
To look at why that's even possible - there's only one Internet. Sometimes (actually, frequently) Cogent's fiber really is the fastest route from one location to another, which is why Internap buys from them and the others (after all, their network is huge, and hundreds if not thousands of home ISP's buy their own bandwidth from Cogent alone.. you can't avoid them, not connecting direct to them just makes those pings even higher). But, Cogent gets a bad reputation as a direct provider for a data center, above all else, due to congestion / routing problems (even though their network is the thing directly connecting most of the users to your game server). That's where how a network gets run really starts to really matter... those Tier 2's I mentioned all use a variety of tools to aid their network in doing intelligent routing beyond the simple BGP routing alone that most do (ie. Internap FCP and various applications of sFlow) that find and attempt to avoid things like congestion. This is how network A gets a good reputation for gaming and network B gets a bad one, even though network A is buying it's bandwidth directly from network B.
There's of course more to it than that when you start to look at direct peering (Mzima for example I know pushes the majority of their bandwidth over direct peers rather than buying transit, while Internap traditionally started with no peers at all), but this should give you some things to think about.