Question

I’ve seen web apps with limitations for user login attempts.

Is it a security necessity and, if so, why?

For example: you had three failed login attempts, let’s try again in 10 minutes!!

Answer 1

Clarification This is a completion to the other answers. Using a good implemented captcha alongside an anti-bruteforce mechanism using sessions for example.
The questioner marked this as accepted assuming that captchas are unreadable by machines (she’s almost right) and so it’s getting negative points, because people think it’s not a complete answer & they’re right.

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Also using a good implemented CAPTCHA could be an alternative way to enpower your application security against brute-force attacks. there’s a wide variety of captcha providers available for free, let’s try the easy way if you’re in a hurry. Also please consider that there’s people outta here saying that "oh, no! this captcha thing is not secure enough and they’re right sometimes!".

"For those of you who don’t know, a CAPTCHA is program that can tell whether its user is a human or another computer. They’re those little images of distorted text that you translate when you sign up for Gmail or leave a comment on someone’s blog. Their purpose is to make sure that someone doesn’t use a computer to sign up for millions of online accounts automatically, or.." ref.