Question: Is there a limit to the number of tiles a city can work? I've noticed that I can purchase and use tiles several spaces away from my city. How far can I go?

Answer: 
Your cities can get to hexes that are up to 3 away from them, although they all have to be contiguous, so you can't get to one that is 3 away until you have one that is two away connected to it. There is no limit to the number of tiles you can work (other than the limits on your population).
The maximum limit is five tiles, but thats for very large, isolated(more resorces) cities and usually your capital.