I keep oak scraps in almost any size over 2" in any dimension. I keep a few pine scraps if they don't have knots. However, I only keep a shelf full in my shop, when it gets more than that, i fill boxes up and put an ad on craigslist to sell a couple boxes for $10. Toymakers and such will come and get them, as they need small pieces anyway. They'd rather pay a few cents a board foot than $2.80.
I buy wood for projects rough cut, random width/length. I pay the supplier an additional $.25 per bf to plane it both sides and straight line rip one side. When I rip to width, I keep all the rips that are 1/4" or more in thickness. I use them for edge laminating plywood shelves and such, and use them a huge amount for shims when clamping things in the vise. I just break them into 18" long pieces and pile them on a shelf near the vise. Wider rips I keep for planing 3/4" or 1/2" square pieces for craftsman type furniture and railings and for laminating up to make stuff. I always go to the smalls pile to shop when i need stuff instead of cutting a wide board.
When I was installing doors, I used the rips for shims when installing frames. An assortment of widths would work better than using softwood wedges.
The primary use I have for small scraps is testing cuts using the router or partial depth cuts on the table saw. Easy to experiment on the same exact wood as the real thing, and see how the cut works or how it looks or see if the depth is set right.
If you do a lot of woodworking, you will always have way more scraps than you need. If you only do projects intermittently, it's good to keep scraps for small needs in between.
dave