Now Twitter is one of the most popular social website. Of course, Twitter clone scripts have been developed, too. Here you can find 5 twitter clone scripts which are open source, so you can set up your own Twitter-like social website without any money.
Laconica Twitter Clone
StatusNet is an open source twitter clone script which is used on identi.ca. Basically, it has the same options as Twitter. It has options like popular, recent tags, invitation and others. It is one of the mostly used Twitter like script. I also suggest to use this.
Official Video About Statusnet
Jaiku Open Source Micro-blogging Script
Jaiku Twitter-like Engine is an open source social microblogging script which a simple but very powerful one. It runs on AppEngine.
Demo | Download
Jisko Free Microblogging Platform
Jisko is an open-source microblogging platform made in PHP & MySQL. It has support for mobile devices, tags, private messages, themes, avatars, mobile interfaces, customized backgrounds, Twitter-like API, also Twitter integration and a bunch of more features.
Sweetter Opensource micro-blogging Application
This is a Twitter Clone Script with Digg like voting. I mean, you send a post and the readers can vote on that. Unfortunately, this software is not being developed now, but you can download and use it.
Of course, there are many other Twitter clones and microblogging platforms. If you know more please share with us.