I’ve read a number of websites that recommend you use Google and Yahoo to see where your competitors receive inbound links, allowing you to go after similar links for SEO purposes. This is smart and can help you keep up with (or beat) your competition in SERPs.
Something else you should always do is sign up for your competitor’s email newsletter if they offer one. If your competitor launches a new service or product, you will know immediately what it is and the price point. You can learn about your competitor’s special offers to make sure your pricing is in line with theirs.
You should sign up under an email address that isn’t explicitly related to your website or your name, as your competitor may simply delete and/or blacklist your email address to prevent you from receiving the newsletter.
If your competitor has a newsletter and you don’t have one, you should consider adding one. I use Constant Contact for my DogWalker.com newsletter, and I think they have a pretty good service. Newsletter marketing is a good way to build brand loyalty and drive traffic to your site.