The irony of launching a game in tiers only to have a forced bottleneck at this point isn't lost on us, but BioWare reassures its players that relief is coming soon: "Due to the high volume of new game codes being redeemed on SWTOR.com, some users may currently be seeing a waiting page. We are intentionally controlling the flow of traffic and letting as many people through as possible."
So if you can't play the game because you can't access your account (or read the forums for updates and more info...), you're not alone. As annoying as this may be to players, it's a good problem for BioWare to have.
[Update: BioWare set up more info on its Facebook page since their main site is down.]