I've done it, converted a 1990 Trek 1100 to 8-speed Shimano 105/Ultegra! Couldn't be happier with the results. A few things:

* You'll need a new chain unless it's one of the newer 7/8-speed types. And you should replace it anyway, it makes no sense to use an old chain on a new cassette.
* Are you *sure* your rear hub is actually a cassette hub, and not an older freewheel hub? If it's a freewheel hub, you'll have to replace it with a cassette hub (rebuild or replace the rear wheel!)
* An 8-speed cassette will NOT fit on a 7-speed cassette hub... BUT you can replace the freehub with a slightly wider one and redish the wheel. This is pretty simple, and the wider freehub only costs about $20 for a Shimano hub.

Personally, I went whole hog and replaced everything on the bike except the frame, headset, stem, and seatpost... but if you already have Shimano components and a cassette hub, it's just a matter of replacing the freehub, the cassette, the shifters, and the chain. Hope that helps!

Alternatively, you might consider using bar-end shifters instead of STI. I love them, and find them just as convenient as STI except in a tight paceline/race situation. They can operate in both friction and indexed mode, and you can get 7-speed bar-ends pretty cheap. I highly recommend them unless you'll be racing. I've been using bar-ends in friction mode for two years on my commuter road bike, and couldn't be happier.