Does Android 2 support swap space? With Android 2.3 being Linux-based, can Android 2.3 use a swap partition without being rooted?
As using swap is a system-wide thing (even on Linux/Unix, you need to be root in order to activate/deactivate swap), this cannot be done without having root access to your device.

If your device is rooted, however, there are several apps available to help you manage swap space. You might want to take a look at e.g. Swapper 2 (for Root users) (free) or ROEHSOFT RAM-EXPANDER (SWAP) (paid, and not really cheap). Both seem to have quite good reputation. Of course there are several other solutions available as well.