You might know that you should delete incriminating e-mails, but it's not always easy to determine whether real permanent deletion has occurred. Still, if you delete an e-mail and empty your deleted e-mail folder, and your significant other doesn't have access to a computer forensics expert and hasn't installed a keylogger, it might effectively be gone. But if you are using a non-browser-based instant messaging client, such as the ICQ or AIM clients, or the host of multiple messaging service clients that are available, such as Trillian or Adium, the software might be storing log files of your personal exchanges on your computer unless you have specifically set it not to do so. Your partner could find and read these detailed transcripts of your conversations. And an industrious spouse could set the program to record history even if you've set it not to do so (again, beware of auto-logins).
These log files (along with e-mails and other private information) could also come up in searches done on desktop indexing applications, such as Google Desktop, which allow a user to search a computer's contents by typing in keywords. Support for Google Desktop has been discontinued, but it still exists on lots of people's home computers, and there are other applications that do the same things out there. And the right combination of sex and relationship related keywords could bring the cheater's activities to light.