OMG! NO!, Syndey. There are so many reasons why not to do that and like, zero, why you should. It's a trap many marketers fall into--"Well my competitor did it and look at their rankings." And then you become the next casualty in the SEO wars. At least you asked first. Many throw the spaghetti at the wall first and then ask questions about their penalties later.
I try to push people to read the Beginners Guide to SEO (and everything else you find) here because it is solid, whitehat information and that can be hard to find out there on the web. (And while I'm thinking about it, do pay close attention to the dates of anything SEO-realted that you read--if there is no date or it's more than a year old, don't waste your time) Fundamentally, it goes like this be patient and learn everything you can for a couple of months before you even think about making changes to your site. The reason is, if you do something wrong, the recovery process could put you/your site into a tailspin that you might not recover from.
Now, back to your competitors' links. Firstly, do you really know that those links are helping them rank, or do you just see them there and assume so? Remember, correlation is not the same as causation, as they like to say here. Secondly, it's not always or necessarily the links themselves that are of value but the pattern of link acquisition that Google pays attention to. If there was a way to view things as Google does, even someone relatively new to online marketing could probably tell the difference between a whole bunch of low-quality links from obtained in a relatively short amount of time (yes you would burn out of your tactic within a few months) and a strong link profile of slow, steady link acquisition from reputable, complimentary sites. If you were Google, which backlink profile do you think you would reward? Thirdly, do you know how many good links it takes to outweigh a bunch of bad ones?
It only takes ONE. Focus on getting that one and you and your site will be way ahead of the game--and your competitors.