There are two varieties of Gigabit Ethernet. One uses SC Fiber--a full-duplex connection composed of two fiber-optic lines, one for transmit, one for receive. The other ("gigabit over copper") uses the same type cables as Fast Ethernet, just stricter tolerances.
Gigabit over copper is limited to 100 meters. I believe Cat6 cable is required for reliable transmission, but Cat5e does well enough if you run your network over a reasonably fault-tolerant protocol (i.e. TCP/IP). I believe (not 100% certain) that gigabit over SC fiber goes to 500 meters, but it can't take much bend radius. Sharp creases in your fiber-optic cabling will not make gigabit happy.
Gigabit over copper is generally much less expensive than gigabit over fiber. Fiber Gigabit cards cost upwards of $400 last I checked; high-quality copper Gigabit cards can be had for less than $200. Cabling becomes an issue as well, as fiber optic cable costs more to manufacture and typically has to be done in a factory with expensive stationary tools--fiber optic cables are not the sort of things you can punch easily out in the field. Cat5e/6 cables, OTOH, can be punched quickly and relatively easily for <$100 worth of hand tools.
Fiber optic hardware is also somewhat more dangerous to work with, mainly in terms of eye damage. Someone getting careless or stupid with fiber optics can get himself permanently blinded.