There are many factors to consider to answer this question.
1. How your monitors are rotated and placed on your desktop?
If those are wide screens in landscape mode, you can hardly have more than two. Just because your eyes can focus at a limited angle, and motion outside this angle will mostly disturb you and decrease productivity.
Actually I have two wide 22'' and 24'' monitors in landscape mode. If I buy a third one, it would require me to turn my head each time I want to look at it. If I can't see all the workspace at once, what's the point in having more monitors?
On the other hand, portrait-rotated monitors fit well and you can have three or four of them, since you will be able to see the whole workspace from side to side.
2. How many windows can you handle at once?
I can't imagine working with more than three windows at once. Just because my brain will explode. Most of my work is done with two only windows:
- two pieces of source code,
- class designer and source code,
- database schema and source code,
- browser and source code.
I can deal with three windows, but it's hard. I can't do it with four. If I'll have four windows displayed at once, I'll just forget about one of them, and "switch" mentally to it when need.
3. What is the size of your monitors?
It's not about the number of monitors, but about space.
I often see in some companies developers working with two monitors, one being 21'', the other - 17'' laptop. Theoretically, they have two monitors. In practice, they don't even have one.
If on the other hand you bought two 26'' displays, chances are you'll not need a third one very often.
In theory, one 40'' monitor will be enough. In practice, it's difficult to rearrange windows on a single large monitor (at least in Windows; I heard in Linux it's much easier, but I don't have enough information on that), and your productivity will be affected.
4. Do you have always-on applications?
As a developer, you may have applications which are always running and it would be helpful to show them permanently. For example, time tracking app can be a good candidate. Bug tracking display with auto-refresh is another one. Ideally, you would have those applications running on a small tactile screen positioned on a side where you can watch from time to time.
Would it increase productivity? It depends. It may be useful to see relevant information permanently for some people. For others, it will rather distract them too much and decrease their productivity a lot.