Description:
Aiptasia are small light brown anemones of the species A. pallida and A. pulchella.  The anemones are typically less than 1.5" long and frequently much smaller.  They are semi-transparent, hence the common name of Glass Anemone.  They are photosynthetic, but will eat things that are small enough for them to catch.  The stalk is attached to a hard substrate, usually in a crevice.  This allows the anemone to quickly withdraw into the hole when danger approaches.  Aiptasia reproduce through the process known as pedal laceration which occurs when baby anemones develop from small bits of tissue left behind as the anemone wanders around.

Good or Bad?
Aiptasia anemones are BAD.  A couple of anemones are not a big deal except that they quickly spread.  They pack a powerful sting that can irritate or kill desirable corals and clams in the tank.  Aiptasia are common pests that most hobbyists have to deal with eventually.  Consider it a rite of passage in the hobby.  Unfortunately, some unscrupulous or unwitting LFS will sell 'anemone rocks' which are rocks overrun with Aiptasia.

What Do You Do?
Aiptasia is most easily controlled when first observed in the tank.  New live rock and corals should be inspected before placing in the tank. Over time, they will spread and make eradication harder.  Control takes 2 main forms:

1) Chemical Control - The anemones are assaulted with an injection or slathering of a caustic substance.  

• A product on the market called Aiptasia Stop is a concoction of pepper juice which when injected rapidly kills the anemone.  I have used this product and it works well when it can be injected.  It is stated to be safe to other tank inhabitants and I have used it around clams, corals, etc. without any harm being done so their claims seem to have merit..  

• Inject with a caustic solution made from a concentrated Kalk solution or similar. 

• Inject with hot (near boiling) water.  

The problem with the injection approach is that it is difficult to get to some anemones to inject them, and they don't just sit around waiting for you to complete the task.  They are very adept at retreating into the rock.  It does give you a certain amount of satisfaction when you do nail them however.  This approach also does not help much with the small ones.

2) Biological Control - The approach taken here is to introduce animals into the tank that will eat the Aiptasia.  There are not a lot of animals that like to eat them however.

• Copperbanded butterflyfish are sometimes good aiptasia eradicators and sometimes they are completely worthless.  It appears to depend upon the specific fish.  I know LFS that routinely rotate Copperbandeds in their tanks to keep the aiptasia in check.  My results have been less stellar.

• Other Fish such as Raccoon butterflyfish also eat Aiptasia, but tend to eat small soft corals as well, so they are not recommended for use in a reef tank.

• Peppermint shrimp Lysmata wurdemanni are small pink to reddish lightly stripped shrimp that sometimes do a good job on the aiptasia.  I have found that some shrimp are voracious eaters and some seem to pay the aiptasia no attention at all.  These have done the job in my tanks and appear to be harmless to the desirable corals and clams for the most part.  There have been reports that they will eat corals that look similar to aiptasia, such as yellow polyps, so this is something to watch for.  The larger adult shrimp may be better Aiptasia eaters than the juveniles per my experience.

• Nudibranches of the species Berghia verrucicornis from Caribbean waters are sometimes used to eat aiptasia.  There is much speculation as to which ones really work and there appears to be much confusion over which ones are which.  In any case the nudibranches die as soon as their food supply is depleted which is unfortunate.

Notes: 
Specifically, I did not mention mechanical removal and with good reason.  Aiptasia have amazing powers of regeneration and cutting, grinding or smashing of the anemones may serve more to propagate the animals that to kill them.