The pool I am with has sent about twenty transactions to one address I gave as a 'send to' addy. Could this one address just go on and on taking more and more of these transactions? A hundred of them? Ten thousand?
You can use it as many times as you like. There is no upper limit.
The reason that people advocate using new addresses is that it increases anonymity. For example, people who know your address can easily look up how much has been sent to it in total. See these questions for some more info on anonymity:
Though there is no limit on the number of transaction received, you might run into trouble when you try to spend the bitcoins that you've received. As stated here:
Because the fee is related to the amount of data that makes up the transaction and not to the amount of bitcoins being sent, the fee may seem extremely low (0.0005 BTC for a 1,000 BTC transfer) or unfairly high (0.004 BTC for a 0.02 BTC payment, or about 20%). If you are receiving tiny amounts (e.g., as small payments from a mining pool) then fees when sending will be higher than if your activity follows a more normal consumer or business transaction pattern.
Others have mentioned that there is no need for a transaction fee to be paid, though you might have to wait a little longer for your transaction to be included in a block (DeepBit was given as an example). However, I've also heard that the Bitcoin Client application (older versions anyway) specifies a minimum transaction fee, which seems to be supported by the above quoted text.