I have 14 road bikes and a single speed.
You need at least 2 of each so that you'll not have to change a tire when you go out in the morning and find a flat. 3 improves your odds and 4 pretty much guarantees problem free riding.
But really, for me it's not about different materials doing different things or special purposes or anything else. For me, it's about paint jobs. I'm a sucker for a pretty face. Well, paint jobs and frame materials to the extent that I've been curious and I wanted to cover the bases - steel, aluminum, Ti and CF.
In the end, I think they all ride the same. The limiting factors are how much storage space you have and how much money you're willing to burn.