Yes, assuming a few things:
1. The network wiring is run using cable of sufficient quality that is terminated properly and is not affected by any interfering factors. Cat5e or better is recommended, although I think I heard regular cat5 is sufficient in some cases.
2. The computers that attach to it have network cards that are capable of the higher speeds
3. You are referring to communications inside your own network (your house). This will not speed internet surfing as that is a much slower connection. Moving big files inside your network though, big improvement.
4. Your computers can get the data out fast enough. If your hard drives a slow feeding the data, the throughput will probably be less than 'full gigabit'.
Overall, if you are setting this up, I figured do it right as you will need more and more bandwidth in the future (and FIOS and other fiber type solutions may quickly increase bandwidth in the future). Even if you do not get maximum throughput your should see an improvement in speed of some sort.
If your computers already support gigabit, and your wiring is new or in good order, the question becomes is it worth $150 for the upgrade. If you need more to get there, then the number just gets a little larger. PCI cards that support gigabit are only $20-$30 if I recall. I had used Intel cards in the past, but most motherboards above a certain quality level contain gigabit networking built in.
I am sure there may be another low level detail or two, but in a nutshell this is it.
I have all my computers hooked up via gigabit, and moving large video files is a lot faster (or anything large for that matter).
Hope this helps.