It depends on how you use it.

For me, a second monitor greatly increases my productivity. I do a lot of research/writing, and being able to have my notes and research materials open on one screen with a word processor open in the other is far more efficient than flipping back and forth between windows.

If I'm being bad, however, I might have IMs, twitter, and whatever other distracting things up on the second monitor, with work on my primary monitor. In that case the second screen becomes unproductive because instead of being easier to see my research, it's easier to see the distractions.

I think the issue is less about the number of monitors you use and more about the number of contexts that you maintain on those monitors:

Single Context: It is possible to configure a monitor arrangement to act as a single desktop area and tile application windows across all of the monitors or at least arrange windows from the same application across multiple monitors - e.g. a designer may have their main document on their largest display and their digital asset browser on their secondary display.

So, in this setup, the displays represent a wallpapering of a single (primary job) context. Switching context involves key-combos, gestures or shutting down the context and starting up something else instead.

Multiple Contexts: I've seen many multi-monitor setups that have multiple applications arranged over a number of monitors, for example:

Primary Display: 3/4s browser, 1/4 for 'task list' (start bar/dock, etc)

Second display: 1/2 email, 1/4 music player, 1/4 Social Media aggregator

There's nothing inherently wrong with this setup, but it allows multiple contexts to compete for your attention. For example, you're researching some topic and a mail comes in about something else. You open the mail.. and you're distracted for a while. You eventually get back to the research then see there's some buzz on your social feeds that pulls your attention.

In all the studies, articles and books on productivity I've read, "context-switching" is the biggest threat to productivity. Sure, some jobs require switching between multiple high-priority items, but that's usually a concerted effort in between larger periods of focus.

In conclusion, multiple displays only impacts your productivity if you fill them with items which will cause you to become distracted away from your goals.

Yes, because of the OS and how open applications are handled.

I use two monitors at my daily job and have to say it allows me to be extremely more productive then only having one monitor. The reason for this is because I am able to separate windows and web browsers to give me real time information and respond to it.

I use one for status notifications and one for my primary work. The status notifications monitor allows me see the bigger picture without having to open and close applications.

Even having one big monitor I don't think would be the same because of the way the OS handles open windows with only one monitor.

I think having three windows might be a distraction.

I don't see any reason why using two monitors could reduce productivity.

I use a vertically-oriented monitor for code, and a standard one for displaying various informations, statuses, documents, emails or IM. One monitor wold be fine too if it is very large.

I think the most important is total screen space.