How many links do I need?

To get a higher PR than them you mean?

Firstly, PR isn't just about incoming links from what I understand. There are some other mysterious factors that go in to that.

Secondly, it's not about quantity, it's about quality. Better to have a few links on some good quality pages than a zillion on low PR pages that don't matter.

Thirdly, it depends on who your competitor is and how competitive the field is. There's no universal answer here

It is not just game of achiving backlinks.. otherwise everyone will start exchanging links with other and reach on top..
[1] you should receive links from unique IPs as much as you can.
[2] Try to get quality of links rather than Quanity
[3] Also try to get links from relavan content.. if you recieve a lot of links from irrelavant pages than you will though away in SERPs
[4] Also depend upon relavancy factors of your web page..

42.

Okay, really it depends on your competitor, and what you mean by beat. If you're just talking about ranking higher than them in the search engines, it varies. If they've been around awhile and have gotten a decent ranking over time, you'll need way more than they have, and from higher ranked sites than their links are on. If, instead, they're about the same age as your site, you just need either more than they have and/or links on higher ranked sites.