I think a good rule of thumb to go by is Valve's whole "breadth + depth" thing... Basically, it's good to be able to compose in many different kinds of genres, because making a living off of game composing requires you to take on a huge variety of projects. However, finding your own voice (something that makes you stand out; something you particularly excel in) is also quite important, if anything, just because there are so many composers out there looking for work.
(No yoshi is an island? xD nice)
Even if I'm a newbie and so far all I have done has been for free I've been asked to compose in zillions of different styles. That is: Rock, metal, goth metal, j-pop, classic, baroque, romantic, jazzy sexy, dub-step, electronic hard-core, medieval epic, valse etc.
What I've learned is that you should try to do everything, but sometimes some styles or specific tunes are just out of your capabilities. Then you only can say: "I'm sorry but I cannot compose in this style right now. Please search someone else" Having to say this hurts