I would say you need a lot of experience, relatively speaking, to dive in the Galapagos.
I was on a trip in October 2009. The dive operator did a very good job (Quasar) of outlining the realities of the trip. Unfortunately, there were people on the boat that did not have enough experience, IMHO. The first "real" dive, we went out in two pangas to the site. The group was "mixed" at this point. It became very obvious on this dive, that some people simply weren't as experienced as they had stated they were. When we returned to the boat, there was a "mutiny" of sorts, wherein the very experienced divers refused to dive with the less experienced. To the captain and senior guide's credit, they reshuffled the group into the die-hards and the less-experienced.
I would say some experience that would be crucial to have is diving in a lot of current. I think we had maybe 3-4 dives in the whole week where there wasn't current. At Wolf and Darwin, you back roll off the panga then do a very rapid head-first descent to grab onto rocks, so you won't get swept away. If you can't do a rapid head-first desent, you'll most likely get swept away (currents are that strong). You will also need a very good regulator that won't free-flow in the current (many will).
In terms of other gear, I dove a semi-dry 8/7 (Aqualung Solaflex), and was quite comfy. The issue is that it took me 32 lbs of weight to be neutral (I am an instructor, and was not overweighted, as I normally wear 8 in my shorty 2 mm). What is very usefull for this is to have a BC with double width weight pockets (I dove my Aqualung I3, which has them). Almost everyone else had massive weight belts.
Also, you need to be very comfortable doing your safety stops "out in the blue". At Wolf and Darwin, we often would hang on and wait until something big came by, then we would follow the guide straight out into the blue, following whatever he saw. We would then spend the rest of the dive in the blue (and current). All fine and well, but you also might encounter massive "down bursts" of current (you swim along, perfectly neutral, then realize your ears hurt. You equalize, then it happens again. You look, and realize you are being pushed downward by the current...so between kicking up and giving a little shot to your BC, stop the downward descent...being careful not to rocket up too quickly once the downburst stops).
Be aware there is no "rescue" at Wolf and Darwin. There are no helicopters on the islands. If you mess up, it is 19 hours, one-way, against a surface current, for the boat to get you to medical help on one of the islands.
In terms of other skills, you really need to have good mask removal skills underwater, and not get freaked out if your mask gets turned sideways on your face in the current. If you're wearing a full hood (which I recommend), this can be mitigated by putting the hood on over your strap. USE your snorkel, as sometimes you come up and it isn't very pleasant top side. A good snorkel is a must. Have a LARGE safety sausage, and know how to use it effortlessly.
Other stuff? Forget any lights, other than a small BC light. Night diving is not allowed.
Forget the reef hook, too. Plenty of rocks to grab onto (bring gloves!!!).
And definitely bring a camera. This place will blow you away.
God bless my panaga driver!!! I gave him the sign when I went up in the waves and he was on top of me in seconds (seemed like forever) but I know he was there quickly.
