Domi lists a lot of great examples of idiomatic expressions. And like he said, they're often interchangeable in sentences like "Was machst/tust du heute?" or "Ich habe das schon gemacht/getan."
I just wanted to add that I've found that "tun" is used a lot more commonly in Bavaria and Austria than the rest of Germany. There are lots of words that are completely correct, but vary by region. If you're interested in a specific region in Germany, you can choose based on that.