Email marketing is arguably the most successful marketing strategy out there. Most companies still don't execute on this well, and the opportunity with automating drip campaigns to list segments are endless.
I am not sure how sophisticated your competitors email marketing strategy is, but it's a no brainer to spy on them as much as possible. For starters, make sure to subscribe to their email list. This way you can see what promotions they are emailing to their list, as well as how often they email, what email service provider they use, and what messaging they are using.
If you want to be a little more sophisticated, and see what types of upsells they promote via email, as well as how they segment their list, buy a product or two from them, and monitor their email correspondence to their customers.
This is free, and super easy, and more importantly, it can give you an edge on their email strategies...
BONUS: If you really want to cash in on your competitors email strategy, you can run gmail targeted placement ads in adwords targeting a unique string of words in their emails, and offer a better promotion than they are. For example, if they email a coupon for 15% off, you can run a gmail ad to that targets the text of that email offering 20% off.
Happy Hunting.