BradB's post has me thinking about competitors websites, what do you look at, and how long do you spend doing it?
I thinking along the lines of content (how much, how well written), site structure, SEO techniques.
As it currently stands, this question is not a good fit for our Q&A format. We expect answers to be supported by facts, references, or specific expertise, but this question will likely solicit debate, arguments, polling, or extended discussion. If you feel that this question can be improved and possibly reopened, see the FAQ for guidance.
I would view the services that they provide, which my website doesn't.
I would view my website's performance in comparison to them.
I would view How user friendly their website is.
I would view the traffic that they fetch and analyze the reason behind it.
I would also view the SEO techniques they use to fetch the traffic.
Then try to improve my site to exceed their service, in performance and in user frienliness.
In addition to Starx answer I would also check sites such as quantcast. They can provide valuable incite into market share and audience.
I start with the structure from the home page. What are the top-level links and what words are used to describe them? As you do this, you have to consider whether the things you are analyzing were done with much consideration or not. You might be thrown off by a competitor who has been successful despite his or her SEO inadequacies.
I've often considered poor page titling logic as a way to determine whether or not I should care about a competitor's technique.
If they pass that test, then I dive deep on details such as the URL string, naming conventions, anchor text (internal), PR shaping (use of nofollow on internal links?), etc.