3 or 4 nights in Florence?

Threecat a minimum which gives you two days.

What does the rest of your trip look like?

I agree that 3 would be the minimum to see the main sights without exhausting yourself. If you ran out of things to do, a day trip to Siena, or somewhere else close by (on the 4th day) might be a nice change from all the cities you are visiting.

We stayed 5 nights and had no trouble filling 4.5 days. We didn't even leave the city. Then again, it may depend on what sorts of things you're interested in and what your complete itinerary looks like? I see that you're going to London and Venice; I might assume you're headed off to Rome after Florence?

As CJean mentioned, Florence is a very good base for some day trips so you could always slip in one of those into day 3 if you felt like you'd covered everything in the city you wanted to. I wouldn't do it at the expense of enough time in Rome (if that's your next stop) though.