Let's make a couple of generalizations before we answer this question:
#1) Any airport that Southwest Airlines initiates service to will realize explosive growth during the first couple of years of that service (ref: Islip, Providence, etc).
#2) Let's discount "room for growth", and focus upon existing circumstances.
With these two thoughts figured in, the two airports, at least in the US, that show the fastest passenger growth would probably be PHX and LAS. The two pretty much run neck and neck passenger total-wise. I believe PHX passed LAS in 1998.
As far as "room for growth" goes, DFW probably has the most, although with their eighth runway in design, and the complaining from the local residents, they won't go much further than that. MCO also has a bit of room to grow, as does good old DIA.
Unfortunately, the O and D airports that could use additional room, like MIA, LAX, SFO, etc, pretty much have to make do with the room they've got, and try to utilize it more efficiently.
Tom in NO at MSY
"The criminal ineptitude makes you furious"-Bruce Springsteen, after seeing firsthand the damage from Hurricane Katrina