For the public interest space: LegalServer [0], PDCMS [1] (NY only), Defender Data [2], Pika Systems [3], CaseBox [4] (notably open source and AGPL), among others.
[0] https://www.legalserver.org/ [1] http://www.nysda.org/?page=PDCMS [2] http://www.justiceworks.com/ [3] http://www.pikasoftware.com/ [4] https://www.casebox.org/
For the down the line court space the companies are much larger: Tyler Technologies [5], File&Serve Express [6], ImageSoft [7], among others.
[5] http://www.tylertech.com/solutions-products/courts-justice-s... [6] https://secure.fileandservexpress.com [7] http://www.imagesoftinc.com/
I have a large spreadsheet with what I think is almost every company in the space, but don't want to post them all here so as to not overwhelm.
I think this is a fair-ish representative cross section of the kind of stuff that is currently out there though.