In most cases, what happens is that Datacenters make agreements with bandwidth providers to haul large connections into their datacenter. The bandwidth is then resold to the occupants renting space in the datacenter (usually the bandwidth provider makes agreements with the individual occupants). The actual bandwidth to the datacenter is usually quite enormous.
For large sites, most move into a datacenter, connect with one or more different providers, which often provide 100mbit or gigabit connections into their racks or cages, which can then be routed and used. In 99% of cases, gigabit is the most bandwidth connected to any one server. In most cases it's 100Mbit (because if you are saturating that with http requests, then the machine should be over capacity anyway, especially if it's not static pages.)
Some webhosts and websites spout numbers like "we're connected via 2 OC12s".. but they really can't use all that bandwidth, because although that is what they are communicating through, it's usually a more limited and connection into their rack or cage. (like 100mbit/gigabit)
So, at a single datacenter, they may have, say, 1 gbps (a very high example, for a large cage, with maybe 250 different servers or so sharing it). Larger sites will have presence in multiple datacenters around the world, adding more bandwidth at each datacenter.
Edit: For example, the graph at the link below is a gigabit switch, which most of the major bandwidth providers that pass through Toronto, Ontario connect to. This is in the datacenter at 151 Front Street, Toronto. If you have a rack or cage in 151 Front, you would get connected to this, contact one or more of the bandwidth providers, and buy some bandwidth off of them, and your traffic would go through this switch, to another provider, and off through their large internet connection.) For this switch, which is the vast majority of the traffic travelling through Toronto, it's only peaking near 2Gbps. Note that Google has a presence in that datacenter aswell, so if you use Rogers or Bell or anything with bandwidth into 151 Front, you are fairly close to Goggle.
http://www.torix.net/stats.php