How much time has passed between the events in Portal 1 and 2?

At the start of Portal 2, it's clear that time has passed. You've been woken up every few months for physical and mental fitness tests, until something goes wrong and you're left in stasis for much longer. How long is Chell, your character, in stasis? How much time has passed between the end of Portal and the start of Portal 2?

Assuming the announcer was reciting the number of days you had been in stasis, as with your earlier 50-day wake up call, "it has been 9 9 9 9 9..9 9...[static]", it has been at least 273 years, or 27,300 assuming the pause wasn't a broken-record effect.

In "The Final Hours of Portal 2" e-book, Keighley mentions that:

One way to further differentiate Portal and Half-Life was to set the game far in the future—at least 50,000 years.

It doesn't explicitly say that Portal 2 was set in 52,000 AD, but the general point was that the events between the two series are so distant from one another as to not interfere.

No exact number has been stated that I'm aware of. All we know is that "hundreds of years" have passed between the end of Portal 1 and the beginning of Portal 2.

In an unused GLaDOS voice line she states that:

Fifty thousand years is a lot of time to think. About me. About you. We were doing so well together. _Source

Referring respectively to herself and the protagonist Chell.

According to the Combine Overwiki, the appearance of wood, paper and upholstery would suggest decades rather than years. Portal took place roughly around the same time as the Combine Invasion of Earth (just after Half-Life [estimated to be 2003]]), Chell was the placed in stasis for presumably approximately 27 years and woken up presumably approximately 2029/2030.

2003: Half-Life, Portal.

2029/2030: Half-Life 2 (and Episodes), Portal 2.

These dates are estimations using information from the Combine Overwiki. The 2003 info is taken from a December calander in Half-Life (Office Complex) and the date is either 2003 or 2008. The 27 years info is taken from the Overwiki, in-game evidence and fan information.