Early in my career, I worked for a magazine whose publisher insisted on having weekly meetings to analyse all the competitive magazines' latest issues. The meeting was not designed to discuss what our rivals had done well; it was supposed to generate ammunition with which to criticise them in front of customers. It was a pointless, negative waste of time, dreamed up by a middle management with no creative ideas.
At the other extreme, football managers often say "I'm not worried about what our rivals did elsewhere tonight, I'm just concentrating on next Saturday's match", and it's preferable for us to be concerned about how our own company is performing, rather than worrying about the opposition. But we can learn from their successes.
When it comes to internet marketing, everything your competition is doing is laid out in front of you, and it makes sense to use all of this information. A good technical article to read is 5 Ways to Analyze Inbound Links for Competitors on Marketing Jive. If you find yourself consistently being beaten in the search engine results by an irritating rival who you ought to be beating, it may benefit you to investigate how they're achieving that.