For my purposes, inside the tank, I like algaes that are attractive and easy to harvest. I dislike algaes that spread easily by fragmentation, or that spread quickly across the rock by holdfasts. IMO, the ones that are especially bad are Caulerpas on the rock because they are hard to contain, and Bryopsis and other green algaes known as "hair" algaes because they spread so easily by fragmentation.
These are some algaes I currently cultivate on purpose in the main tank and consider "good": Sargassum (attached), Gracillaria, a rock-growing Halimeda, a sand-growing Halimeda, and Penincillus (shaving brush) in the sand. I've also kept Caulerpa in the sand but it had to be tended very frequently to keep it from spreading to the rock so I eventually got rid of it. In a refugia I'm keeping Chaetomorpha, Gracillaria, free-floating Sargassum, and a little Caulerpa. All of these get harvested on a regular basis.
I have many other algaes that have shown up incidentally by bringing in live rock. Most of these are attractive and spread slowly or don't make a problem of themselves. A current "problem" algae is a short, soft, hair algae which spreads readily by fragmentation.