A buddy and I have brewed a few batches of beer and they tend to have similar flavors when we're done. Could this be attributed to the water? What are some tests you would recommend doing to ensure the water doesn't cause off-flavors?
It certainly wouldn't hurt to know what's in your water. It might not matter to you as much right now, but once you hone in on your process and begin experimenting with recipes, knowing your water profile will help you fine-tune your mashing (if brewing all-grain) and fermentation processes, and ultimately, your flavors.
Things you'll want to test for include water hardness, pH level, and chlorine, among others. Water hardness and pH will affect your mash, and chlorine will contribute to off-flavors in the beer.
If you have your own well as I do, then you ought to know what's coming from your tap regardless. There are a couple of different tests that you run - the CDC has a lot of good information on how often to test, and what you should be checking for.
That aside, there are some micro-nutrient requirements for good beer, and different levels of water hardness will definitely affect the final flavorings of your brew. I have a few books (currently inaccessible) that have guidelines for water quality, but these are a very good set and correspond to what I recall semi-offhand.
I suspect that @Matt means spring water, not distilled water - it's too pure to make truly good beer, oddly enough.