Well, I am not sure any of the above posters actually own one, but we do, so I will try to give my $.02 below.
We have a 1979 Morgan OI 33 (see our blog on the boat sv.islandzephyr.com) and I wouldn't think that a boat built by Charlie Morgan would be of poor quality, and I haven't found this to be true myself, but they are slow, or more like lethargic, which is fine with us.
A few points I would make about the OI.
Each boat is built with a specific purpose in mind. I have found there is no good all around boat for every purpose. The Out Island was built for Florida to Bahama-Caribbean cruising. You can see the exact stats of the 33 on our blog (go to the link for "history"), she has a 3'11" draft, perfect for the "Islands", but even with a full keel, I wouldn't say it was ever built for deep water at all, that wasn't her purpose.
Her purpose was to be able to get in and around the shallows of the keys, not sail to England from the East Coast. I personally ran our Chrysler 26 aground so many times up in the Pamlico River, breaking the keel, rudder, outboard, etc etc that I would have LOVED to have had our OI over there, it would be a great boat for that area as well.
They are slow, yes, but you are SAILING, if you are in a hurry, you can fly?
We had two other sailboats, a Chrysler 26 and a Catalina 22, both of which were way faster than this boat, but both also had their limitations as well. We wanted one we could learn on in larger bay waters and still be able to sleep comfortably on while we are anchored or in our slip.
The are very roomy inside. Our previous two sailboats gave me a terrible backache from bending over all the time (I am 5'10", not tall) and the head room in here is almost 7 feet. The beam is so nice that my wife and I can spend a good deal of time on the boat and not bump into each other every time we turn around. If you spend a lot of time at the dock (as we do at the moment because of our Perkins) it is GREAT to have this beam and headroom.
The comment about them being bullet proof I have to say are pretty close to accurate. I can break just about everything I touch and this boat is very tough and from my time spent on board you can beat the heck out of the boat and it doesn't seem to bother it at all.
They normally have a 50hp Perkins, which is a good motor to have in a boat this size. Ours when we bought it (unknown to us) had a blown bad heat exchanger ($700) and a blown head gasket (about $2-$3k). The heat exchanger we fixed, the other engine problems we will have to wait until we can fund them, but it starts up every time and runs smooth. If you buy one with a 35 year old Perkins I would recommend having it checked out by (an independent) diesel mechanic that knows the Perkins specifically. Our was checked out by a local mechanic to the marina but no one every ran it up for longer than 30-40 minutes. It wouldn't start to overheat (due to the head gasket) unless you ran it that long, so it was never known until we bought it. The engine has been our biggest problem thus far and keeps us from sailing her right this minute.
The other comment about needed to be fixed up before going longer distances I would probably agree, but don't think that is specific to the OI. Any 30-35 year old boat is going to need intermediate or greater care, upkeep, maintenance, etc etc. For some of us on a very very limited budget, the OI is a great boat, especially if you don't have the $50-75k range to spend on a boat. I believe you can get a Morgan OI for around $20k in fairly good condition, and for $20k I personally think it is a lot of boat for the money.
As far as sailing her to the Caribbean, our boat has already been there. Not with us on it, but when we bought it, we found a GPS with the tracks and waypoints still loaded and it went all throughout the Islands. The route was from Tamps, through Lake Okeechobee and down throughout the Islands going south. It had also been sailed up to the Chesapeake Bay area but not on the same trip. This was not 25 years ago when she was young, but 3-4 years ago.
We had ours delivered from Tampa to the Alabama gulf coast and the delivery captain said he was quite surprised at how well it handled the gulf (and he wasn't a big fan of the OI either).
This boat happen to fit our needs, it was in the price range, structurally sound, larger enough, could sail to the Islands with the right upkeep, is a fantastic boat to stay on while working on repairs in the slip, can be handled by two easily, and it gets us on the water.
If I had $40-$60k to spend on a boat I would probably have bought a different boat, but we didn't, we had just enough to buy the OI, and we looked at a ton of other boats in the $20k price range and this was the best boat for the money at the time (May 2007).
Good luck on your search, we for one love our OI, even if other people think it looks like the ugly duckling.