The house I just bought has three different outlets in the walk in closet!! I want to remove a couple of the plugs and just put a solid plate on them. The outlet has 2 black wires and 2 white ones. It also has a ground. Do I wire the black wires together and the white ones? What do I do with the ground?
Yes, if you have your heart set on removing them, then after you remove the outlet, tie the two black wires together with a wirenut, and tie the two white wires together. That way, you will still have power going to wherever the next electrical box is.
For the ground, you can either screw it to the box, if it is a metal box and you can find a place to do that, or just leave it unconnected in the box. If you have two ground wires (one entering the box and one leaving), tie these two ground wires together.
Don't forget: before you remove the faceplate and start removing wires, disconnect the circuit by turning off the appropriate circuit breaker, and then test to make sure that the outlet is dead.
The OP is probably fine with Ben's answer, HOWEVER, you should only nut the wires together if you are sure that they were previously connected, E.g, had taped-off the same outlet (that still had its linking bar intact).
Two blacks and two whites could mean there is multiple circuits present. If turning off one single pole breaker killed all the power in that box, you're good to go; nut them. (Assuming it's not a switch leg, and no other breakers are off in the main panel or any sub panels.)
Back-feeding across two breakers on the same phase is bad (effectively circumventing the protection), crossing the two phases of your incoming is (burn your house down) worse.
Extra outlets that aren't unsightly only add value to your place, and adding a switch box cover to your current hole isn't really going to do much to change the aesthetic.
If you are worried about a coat hanger or something accidentally getting stuck in one, just add a childproof outlet cover and call it a day.