You have lots of choices of native fish that do well in ponds. Be sure to check state regulations to see what you are allowed to stock; some natives and exotics may be prohibited.
The traditional stocked recreational pond has a balance of largemouth bass, sunfish (usually bluegill, pumpkinseed, redear, and/or green), and sometimes a smaller forage species such as golden shiners or fathead minnows. Your state fish and game agency should have info on proper stocking of such a pond.
Other native options include channel cats, blue cats, or bullheads; gar; bowfin; perch; pickerel or pike; and a number of smaller species. Commonly stocked exotics besides koi and goldfish include non-koi varieties of common carp; grass carp; ide; rudd; bitterling; and weather loach.
If you have very large, deep pond you might be able to keep some monsters that demand a bit more space, such as paddlefish; sturgeons; and muskellunge, and fish that need to keep cool, such as burbot; walleye; sauger; and trout.
The deeper your pond is the more stable the temperature will be. Your fish and game agency should be able to tell you how deep your pond needs to be to avoid winter kill. It is also a good idea to run a de-icer, aerator, or water feature during cold weather to keep a hole in the ice so you don't have oxygen depletion problems.