Currently the ISS has two basic segments, the Russian and US sides.
The Russian side has 4 docking ports. Usually occupied by 2 Soyuz, 1 or 2 Progress freighters or an ESA ATV vehicle.
You can see in the picture the tail end of Zvezda has the ATV, the two ports on the front end of Zarya, and then the earth facing (Nadir) side of Zarya. (I see in the manifest that the Pirs docking compartment will be discarded to make room for another MRM module in 2014-2015. Which is another question I will ask, why not move Pirs to the top of the front end of Zarya?)
The US side has three PMAs (Pressurized Mating Adapters). One connects the US and Russian segment together and is permanently occupied. One is on the far end of the Harmony node where the shuttle used it to dock. The third has been shuffled a bit as modules are added, and is on Tranquility (Node 3) now.
The PMAs adapt a CBM (Common Berthing Module) port, to an APAS port that the shuttle can use. The current crop of cargo vessels, using the US side (HTV, Cygnus, Dragon, thus excluding the ESA's ATV), use a CBM since the 'door' is wider and they are berthed by the Canadarm2.
The planned CCiCAP/Commercial crew vehicles all plan to use the PMA (after SpaceX delivers an adapter on a Dragon flight in 2014) for docking.
But as the image of 6 vehicles at the station shows, those ports are getting pretty full. The ATV and Progress vehicles hang around for months, tying up a port, as they are used to dump waste to burn up on reentry.
So far, Cygnus and Dragon has used the nadir (earth facing) CBM on Harmony (Node 2). From the image, showing the HTV docked to the zenith (space facing) CBM on Harmony, it seems like both CBM ports are usable.
Will there come a time where the available ports will not suffice? It seems likely that a US crew vehicle will remain on station as a lifeboat on a regular basis. (NASA seems to be thinking of launching with 4 crew instead of 7 that most plan to handle.)
One imagines a cargo vehicle will remain for a while as well on the US side. That quickly ties up two of the available 4 ports.
It seems like ports at the station may get tight as the station gets busy, but maybe there is enough room.
Of course space is one issue, the other is the available time in the schedule for the crew to deal with visiting vehicles. Rotating a Progress every 3-4 months, an ATV every 18 months, an HTV every 18 months, Cygnus and Dragon a total of 20 visits over 4-5 years, and suddenly that is a lot of vehicle ops, and that seems to occupy the crew a fair bit when it happens.
Seems like automation is really important to get working, going forward.