You need at least one million spinnerbaits.
Seriously though, it depends on a lot of factors (e.g. type of water you're fishing, depth you're gonna be fishing the baits, etc.). I probably have about 30-40 spinnerbaits, but I don't use them all that much except sometimes when I'm fishing the edges of weedbeds or sometimes in submerged trees and such. They're also great for night fishing.
Probably a good all-around spinnerbait size (this is very generally speaking) is a 3/8 oz, white for clear water, chartreuse for stained water, black for muddy water (I prefer multi-hue skirts like white/grey or chartreuse/red, etc.). The standard deal is willow-leaf blades for clearer water, single colorado blade for muddy water and night fishing. There are so many variable for spinnerbaits that it's pretty ridiculous: different variations and numbers of blades, sizes, skirts, arms, etc. That's probably one of the reasons that they're so appealing.
You can find several articles on here for spinnerbait tactics. One thing that IS a rule is that you need to buy a quality spinnerbait. I have some old cheapo spinnerbaits that I used once or twice and will never use again. It's really tough to tune them, so they're always running crooked, and they have poor skirts and dull hooks. Not a good combination. Terminator, Strike King and Booyah all make quality spinnerbaits. For an decent spinnerbait it will cost you 3-5 bucks, but it's worth it.
One last word of advice is to use a trailer hook. I know some people don't use them and still have success, but I for one feel naked without that trailer hook. Half of the fish I catch on a spinnerbait got themselves hooked just on the trailer hook.
Back to your question though, how many you'll need depends on the lake where you plan on using them and the conditions there. Read up on some of the articles on the site for which specific types would be best, then buy a couple in different sizes and colors. If you really like them, then buy as many as you can afford. And if you're ever feeling a little down on life, go to your favorite fishing store, buy a bunch of lures, and you'll feel better in no time ;D