I always advocate classical training for all musicians, even if they don't ever want to play any "truly serious music". Though I have no formal music schooling myself, I've benefited tremendously from the exercises in Simandl's bass method and playing random themes from a classical fake book. I may only be good enough to be asked to join some amateur classical performance once every few years, but it helps with everything else I play.

The reason is that Western serious art music is as far from an actual style of music as it can get. You have to acquire the skills to play things written by hundreds of different people over the span of more than a thousand years. That's a lot of different styles and approaches. Many of these people weren't writing for your instrument or didn't care about making your parts convenient. That means you have to be comfortable in all keys, across the entire range of your instrument, in all kinds of rhythms etc. Playing material written for different instruments or voices helps further - if you play violin then trombone etudes might force you to practice some really inconvenient fingerings while voice parts from opera arias will teach you to be convincingly expressive. Music theory is also very useful, as it describes what sounded good to all those composers and why. Improvisation is the only major skill missing from typical classical training.

This is no magic bullet, of course - I still can't play jazz worth a crap, though I have no problem improvising in other styles - but it's the best you can do to prepare yourself, especially for those times when you have to play unfamiliar styles or when something unexpected happens. For example, your band's pianist decides to mess around with a hammered dulcimer he can't actually play and ends up in the key of C# minor. It's good to have the ear to find the key quickly, the ability to actually play in this key comfortably, and the knowledge of theory to add a sense of direction to those dulcimer amblings.