What does matter is the nature of the plugins themselves. If the plugins are properly coded and serve their individual purposes well, then it shouldn’t matter even if you have one hundred of them active. If the plugins are big, bloated, and poorly written then you could run into a problem with only two active. The key here is the number of active plugins is unimportant; only the quality matters.

This is true, although I think you have a problem if you’re running 100 plugins, but that’s another matter.

The thing to take away here is that you can run how many plugins you want, just make sure they are well-written, then you won’t have any problems.

With that said, I still say you should keep your plugin count down.

To me, it isn’t the overhead a non-perfect plugin might add to your site that is the problem, nor is it any possible increase in http requests and whatnot that it might add. All these things are either only noticeable when using the admin, or manageable with caching. No, the problem, or problems really, are these:

• Plugins get abandoned. This means that the awesome well-written plugin you’re relying on suddenly uses deprecated WordPress functions (which means it isn’t all that well-written anymore), and then it might even break your site since it doesn’t work after an update. The more plugins you rely on, the bigger the risk that you’ll end up in this situation.
• Plugins could end up being a security risk. You know that whole Timthumb thing? Well, it can happen, and if you don’t keep your plugins up to date then you are definitely in trouble when a security exploit surfaces. So keep your plugins up then! Well, what if the developer is sick and the update takes an extra week? Or what if you’re on vacation somewhere without internet access, and come home to a site full of malicious code? Shit happens, and avoiding it could be a simple case of eliminating the amount of possible ways for it to happen.
• Clutter. Seriously, adding feature upon feature just because it is so easy with plugins isn’t a good idea. You’ll do what you please with your site, but just because you can add a cool plugin doesn’t mean you have to.

I have no problem with running a lot of plugins when it comes to performance, assuming the plugins are well-written and that you utilize caching plugins (!) to make sure things run smoothly. I do think you should stick to what you need however, because of the reasons above. Especially if you are less interested in tweaking and fiddling with your site. I’ve gotten too many panicked emails and phone calls from former clients telling me that their site is all messed up, and traced it down to a plugin that broke, often because they haven’t kept it up to date or because the developer hasn’t. You and me probably know this, but the vast majority of customers and users see these things as something you set and forget, which it obviously isn’t.

You shouldn’t run too many plugins, just the ones you need. If that means 3 or 35 plugins activated is less important as long as you keep an eye on them in terms of updates and further development.