Re:
The big question is what hub do you have?
As has been said, its probably a cassette and not a freewheel. In fact I'm pretty sure there are/were no 8 speed freewheels or if they are they are pretty hairy - the extra width means there is more stress on the bearings (which are located close to the spokes) due to the long cantilever.
Assuming you have a cassette hub, the next question is whether it's uniglide or hyperglide.
I believe that 7speed hubs were only ever available in uniglide so you need a hyperglide cassette. However hyperglide won't fit on uniglide freehub due to an extra wide spline. As mentioned previously Sheldon has all the information you'll need.
There will also be the question over rear spacing - 7speed were generally 126mm spacing but 8speed and up were mostly (if not all) 130mm. Alot of people just spread the dropouts as 2mm either side isn't much for a steel frame, but if you've got a carbon frame then that's a bad idea. I'm not sure about aluminium, but judging by the amount old Alan frames used to flex I'm sure it won't be a problem
You have several options if you have a 7sp hyperglide cassette.
Get a new freehub. SJS have a few for old shimano hubs at around £20 a pop.
Use the 8or9 or even 9of10 trick. As the 8,9 and 10 speed cassettes have the same overall cassette width you can remove one cog and one spacer to bring them down to the overall width of a 7speed cassette and therefore fit them on a 7 speed freehub. However this would require matching shifters to make sure they index with the right spacing properly (the last click is then redundant) and you'll end up paying more for the shifters than saving on a new freehub.
You could also just buy a new 8sp rear wheel on ebay.
Also worth noting is all shimano rear derailleurs work with all speeds except 740x Dura Ace so your 8sp rear mech is the same as a 7sp. The difference is purely in the shifters which have an extra click and shorter pull for each gear (because the spacing of the cogs in the cassette is smaller)
My advice would be to check which rear hub you have and go from there.