Twitter, and indeed all social media, is often touted as THE place for creating buzz about your product while keeping your purse strings tight. While there are many ways to leverage Twitter (and many more ways to get all excited about it and end up having nothing but a pathetic account for your product with a handful of followers), hashtag campaigns are definitely one of the more effective means of using Twitter.

Hashtag campaigns are Twitter campaigns where users are encouraged to tweet with a certain hashtag, which, if sufficiently popular, can make it to one of the top btrending topics.
I feel that there are three essential elements to running a campaign on Twitter well:
1. Employ hash tags well i.e. ensure people use the hashtag on every tweet, the hashtag is not too long and unwieldy and at the same time is representative of your product and/or positioning
2. Have a competitive angle for the tweeters
3. Create an exciting incentive structure for tweeters

Hashtag campaigns with monetary incentive
Launch a limited duration hashtag campaign to create buzz similar to what Squarespace and Moonfruit have successfully done.
Squarespace launched a very successful twitter hashtag campaign where users were asked to send tweets with #squarespace and 30 random candidates would get 30 Iphones. Within days, #squarespace became the top trending topic on Twitter.
Their rival moonfruit launched a similar campaign with equal success.

Hashtags campaigns with non-monetary incentive
USAToday recently launched a successful hashtag campaign where users were asked to send #AmericaWants tweets stating which charity should get a free full page ad in USA Today. The charity with the most tweets won while USA Today ot all the CSR-heavy buzz that it wanted.

Hashtag campaigns for crowdsourcing
Launch a campaign encouraging people to tweet about the content (e.g. local news) that you need to source and ask users to hashtag their tweets
Unlike the earlier campaigns which would be time-bound, this would have to be an ongoing contest with a prize given out every week or so. Executed successfully, it could help source content while creating the necessary buzz.