I have the same anemone as dleko and mammoth pictured. They have neither moved nor replicated. One small one got buried by an enterprising mantis.
Of the links posted by mammoth, only the last one (reefcorner) shows a picture that is similar (if not identical) to the anemone here. The reefcorner site identifies this as either Aiptasia pallida or Aiptasia pulchella. None of the other links have photos that look like dleko's anemone.
Take the following disclaimers: (1) I have a degree in biology, but that was more than 20 yrs ago, and we never studied anything larger than a bacteria; (2) the internet is a great source of information and misinformation (not to mention disinformation).
That said, Aiptasia pulchella has a rather dim picture in the about.com site, in Hawaii. I'm unable to find a source that states that A. pulchella has a range in Florida/Caribbean; it appears to be a Pacific species. (Of course, I don't think anyone is doing DNA sequencing on this...). Debi Hauter's picture of A. pulchella does not appear similar to dleko's anemone.
There are many photos of A. pallida on the net, including the seaslug forum. All the other posted photos of A. pallida differ from the photo posted in reefcorner.com. A. pallida does range in the Florida keys. I have seen no source that says it ranges in colder waters (or doesn't, to be fair).
I think reefcorner may not have a correct identification.
I think the Curlycue (Bartolomea annulata, I believe) is more similar, but is still an incorrect ID (too many tentacles compared to dleko's anemone.)
What makes a pest is not whether it's in the Aiptasia family or Aiptasia genus--what makes it a pest is that it replicates, wanders, and stings. Some folks consider (perhaps tongue in cheek) Xenia corals to be pests!
For this case, I don't think it's a pest anemone. Mammoth disagrees, because his (I'm making a gender assumption here, forgive me if I'm incorrect) anemones have replicated. I would suggest terminating the anemone if you don't like them.
I'm in favor of 'innocent until proven guilty.' I have dleko's anemone. It hasn't replicated, propagated, or moved, so for me, it's innocent. I have at least one mantis left in my display tank, about 2" long. So far, it's beating up on barnacles, pods, and eating leftover frozen brine or other fish food. So that mantis is also (I think) innocent (no mayhem in the tank that I can see). The 'gorilla' crabs, on the other hand, are guilty, because I've witnessed them going after snails and limpets. Red emeralds are also guilty (picking at corals).
Off topic: I (used to) get seriously bent out of shape when someone would post a cup coral picture in New Reefkeepers, and 15 people would say "It's aiptasia, man, kill it quick!"
