Other than chain length, what are the limitations to the number of gear teeth? I need to replace my chainwheel and cassette, and it made me think. I know that the chain has to be a specific length relative to the number of teeth on the gears.

I was thinking about changing the cassette for one which a bigger 1st gear. Suppose I could get one with whatever number of teeth I wanted. 

The bigger the better, right? If better means less effort to climb hills. But I have never seen a really big gear, like almost the circumference of the wheel. 

I assume that's for a practical reason, not just because it would be very lazy if it worked and look ridonkulous :)
In the diagram below (from Park Tool) one can notice that if the innermost (lowest) cog grows much larger it will interfere with the top pulley on the rear derailleur. This is the primary limiting factor for the size of cogs.

(source: parktool.com)
For chainwheels, I suspect that the ground would be the physical limit (for a typical diamond frame, anyway).  Of course you'd better eat a good breakfast and have a friend with a shed on his car if you plan to turn a ring that big.