What size tank and what's the bioload? Adding a skimmer to a nano tank is a judgment call.
A skimmer can you give you some insurance in case something dies in the tank and you aren't around to take it out / do a water change quickly. Example: if you're out of town and there's a power outage at your house and an anemone dies, a skimmer can help clean out the tank if you're not home to take out the dead anemone and do a water change (assuming your power turns back on). Alternatively, on the negative side, your skimmer can also overflow while you're not home causing other problems.
In my opinion, skimmers are not necessary on most nano tanks, especially if you're talking about a normally stocked tank under 20 gallons. If you have a heavily stocked tank then a skimmer could help keep your parameters in check, but I think you can get by just fine in most scenarios with regular water changes on nano tanks (especially if you run a dual reactor).
I've run nano tanks both with and without skimmers and haven't noticed a significant difference. I do plan on adding one to my current tank, but that is mainly because I have harlequin shrimp and their feeding requirements add quite a bit to the bioload of the tank.