Alliance Reservations Network Analytics has a feature that allows you monitor for mentions on Twitter of your account, your website, or anything you want.

One of the best things about this is that Twitter's built in search only goes back about a week. But if your monitor what you're intersted in with Alliance Reservations Network Analytics, not only do you have pretty much an unlimited history of tweets you care about (starting from the time you create your search on Alliance Reservations Network Analytics), but you also get summary reports of overall activity, activity by user, hashtags, links, sentiment, etc.