A couple of things:
Some of the questions in this thread show zero understanding of household wiring and the safety practices that go into it. As such, you REALLY shouldn't be messing with it. You are about to make the most basic mistakes and potentially disable all the safety systems that you currently have.
The white (neutral) and bare (ground) coming together to the same terminal strip in your electric box is normal and correct, but note that the main breaker box is the ONLY place where the two are allowed to come together. You can't join them anywhere else in the house or outbuildings. As a side note, people installing generators almost always mess this up.
A 220V circuit is either split phase, or single phase. In a split phase circuit, there are 4 wires: Line 1 (black), line 2 (red), neutral (white), and ground (bare or green). From a split phase circuit you can extract 220V between L1 and L2, and you can extract 110V between L1 and N or between L2 and N. In a single phase circuit there are 3 wires: Line 1 (black), line 2 (white), and ground (bare or green). In a single phase circuit you cannot extract 110V because there is no neutral. Also, unlike a 110V circuit, the white wire is NOT neutral. It is HOT and can knock you on your butt or kill you, just like the black wire.
As to the original poster's question, nobody asked but it sounds like you have a single phase circuit. If that's the case, you cannot get 110V by rewiring the outlet. You can, however, rewire back at the electric box to make it a 110V circuit (changing the outlet appropriately as well). You would need a new single pole breaker (the 220V circuit will be on a 2 pole breaker). The white wire will become neutral and be wired to the terminal strip with most of the other white wires, and the black will go to the single terminal on the new breaker. You will also probably end up with an open slot in your breaker panel which needs to be plugged with an appropriate filler plate.
Someone else suggested using the ground as a neutral - after all, they are wired to the same terminal strip in the breaker box, right? I don't mean to be harsh, but this is the most basic mistake make by someone who knows nothing about household wiring. The ground wire should never under any normal operating condition be carrying current, which it will be doing if you use it as the neutral, or tie it to the neutral anywhere other than a single point at the main breaker panel (remember that rule from the first point). The only time the ground carries current is when there is a fault. It's there solely for protection.
Hope this helps, and stay safe. It's not just you, but also the unsuspecting guy who comes along after you expecting things to be wired properly only to find out the hard way that they are not.
