What footwear for outdoor activities should I own?

I hike 10 to 20 miles in a typical week, backpack a few times a year, camp, and just started climbing. I'm moving toward more technical mountain summits, but nothing intense enough to require mountaineering boots or crampons (yet).

I currently have these:

Timberland boots

Approach shoes

Climbing shoes

Winter boots

Microspikes

I want the right tool for the right job, but I'd like to get away with as few shoes as possible.

Which ones do I need, and which can I live without?