During the past weekend my target was to finalize "Explopool" flash game. Basically, the game mechanics was working pretty well and the content was also in good shape from my point of view. However, I found some flaws in the first tests and decided that overall gameplay was not on the satisfactory level. Therefore decided to postpone the release date and started to do some major modifications to improve gameplay and overall look&feel.
Testing your game is extremely important, especially if you are going to make a public release of it. Although your brand new game seems to be finalized on the surface, it is very probable that there is still some polishing to do and in most cases also some bugs to be fixed. Finding those may require very intensive and creative testing.
Common target for game design and testing is to make a game that will be a positive experience for the end user. If game designer (=you) is the only tester, then it is very probable that the testing experience is not comprehensive. Thorough testing will require multiple testers to get better coverage for different corner cases: You are playing the game your own way, but some other may play it totally different (and possibly unpredictable) way that might cause some unexpected behavior. The more testers, the more likely critical flaws are found before releasing the game.
But where to find testers for your indie game? I have used "family and friends" approach for testing my games, and surely that has helped to get the most critical bugs out from them. However, this kind of testing has not been thorough enough and I have to admit that few nasty "features" have ended up in the released games. Of course you can do bugfix releases, but it is not a good reputation if your game has lots of bugs in released version(s).
Currently, I am trying to find out feasible ways to get more testers for my upcoming games. I am not too sure how to implement this in real life, but one idea is to make some kind of a "limited release" and invite set of individuals to play game and give their feedback about it. Target is to improve the overall quality of released games, so first I have to learn to tolerate smashing feedback. :)