This subject is a can of worms! The trouble is, the term "isolation transformer" means different things to different people. And, there is a massive amount of misunderstanding out there!
I will assume that we are talking about an electronics workshop:
It is a mistake to regard an isolation transformer as a safety device. OK, you can touch either side of the secondary and not get a shock - assuming that it is truly floating, and hasn't become "earth-referenced" by something plugged into it. But,
the isolation transformer is simply to allow the connection of grounded test equipment (e.g. a 'scope) to a Device Under Test. Normally, this is only required for limited aspects of maintenance (or design, perhaps) - such as when you need to look at the primary side of a switched-mode power supply, for example.
The rules are:
1. Only one DUT connected to the transformer output.
2. The earth connection should not be carried across (though most commercially available units do, sadly).
In the old days, TV sets and radios had a live chassis, so isolation transformers were an essential part of a maintenance workshop. Those days have largely gone, so unless you're working on vintage gear, isolation transformers are only occasionally useful (as mentioned above).
It's easier, safer and cheaper to use an RCD most of the time.
As mentioned, other uses of isolation transformers exist. For example, some use a transformer with a centre-tapped secondary, with the centre-tap grounded. This means that the magnitude of an electric shock will be reduced, as now the greatest potential between earth and a "live" conductor is now half the mains voltage. Of course, those yellow "site transformers" that you see on building sites work that way. But in an electronics workshop, an RCD is still easier, safer and cheaper here.
Others violate Rule 1 by setting up an "earth-free environment". This is complex, and not worth the effort in most cases. I've never met such a setup directly, but have spoken to people who have - none of whom have managed to convince me of the merits.
Another use of isolation transformers is to remove the leakage current of the devices supplied. I know of some OB vehicles that do that, for example. One side of the secondary is connected to earth, creating a live and neutral so that the RCDs on the vehicle can work, so on the face of it, why have the transformers? But tripping the RCD inside the venue is normally embarrassing!
Finally, remember that generally, large transformers are a pain. They are incredibly heavy, they take valuable space, they generate heat, they are normally mechanically noisy, and they are something else to go wrong. So think carefully before getting one...
Mine are here:
http://www.markhennessy.co.uk/isolating/index.htm