Year-round would be: denim and chambray, french terry, flannel/brushed cotton, oxford cloth, jersey and rib knits. Most cotton fabrics, to be honest. I don't rely on any of these in extreme heat or extreme cold, but they do get wear in every single season. For me it's mostly a matter of making good use of baselayers once it gets chilly. Heat doesn't bother me much, but I run pretty cold. Except for heavy wool sweaters and long coats, most of my jackets and toppers are useful even in the summer. I have a couple cotton field jackets and a denim jacket that I don't wear in the winter because they just aren't insulating enough.
Recently I've been getting more mileage out of cashmere and wool early in the fall and late in the spring, because once the winter heating season is in full swing, my skin gets very dry and easily irritated so I tend to avoid animal fibers as baselayers during the coldest months (ironic and frustrating, I know).
I'm very open to the idea of thick, nubby linen for cooler weather (or linen blended with silk or wool), but it's tricky to find.
ETA: I don't have any velvet at the moment so can't speak to that, and only one pair of corduroy pants. Corduroy seems fine to me at any temperature when heavier denim is (and most of my denim is on the thick side).
