Are you talking x1 slots or x8 slots because it makes a difference.
These are the different size PCIe slots. If it is the "smallets" you've ever seen, then I would guess you have x1 slots as those are on a lot of motherboards. You can buy PCIe x1 slot cards from
newegg
EDIT: did a bit of reading, a x16 card will work in an x8 slot, but typically the x8 slot isn't open ended. You can buy a converter, or you can just "fix" the slot so it is open ended.