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UPDATE: In the 2013 episode "Journey to the Centre of the TARDIS", this question is finally answered when the Doctor states that the interior of the TARDIS is infinite (this despite, as noted below, classic-era statements regarding percentages of the TARDIS). What follows is the earlier archived answer to this question:

On TV, they've never said one way or the other.

Some stories seem to imply that it's not infinite, just very big. UPDATE, most recent one said its infinite. For example, 25% of the TARDIS was burned up to provide additional thrust in the original series episode "Castrovalva". However, this may just mean that 25% of the infrastructure of the TARDIS was destroyed, but the available space in the TARDIS is infinite.

In non-TV stories, it's been explained that the TARDIS is potentially infinite, but not actually infinite. It isn't ever explained exactly what this means, but one possible interpretation is that, because the Doctor can create new rooms on the fly, the TARDIS can restore rooms from storage (even rooms that haven't been stored yet), etc., there's no limit to how many rooms there could be, even if at any given time the number is finite.

Behind the scenes, Steven Moffat has said: "I like to think the TARDIS goes on forever, in many strange and scary ways."