I built and run DocketDaily (
http://www.docketdaily.com). We mine and process litigation data which is used for a number of law-related purposes. As others have mentioned, Thomson and LexisNexis have the law firm market nearly locked down (for the time being, at least, as even this is changing), so we decided to target a slightly different space. We focus on legal vendors -- those selling into law firms and in-house counsel -- and provide them with very useful data and information for their sales/marketing efforts.
This strategy -- not targeting the law market head on -- has proved beneficial, and has allowed us to establish a base from which to expand to adjacent verticals (law firms, in-house counsel, legal recruiters, etc.)
We have a few competitors (Lex Machina, DocketNavigator, LawProspector, others) but they each tend to carve out a niche. In the case of Lex Machina and DocketNavigator, both are entirely focused on 1) law firms, and 2) patent litigation. It's a big world out there, and data in law is relatively young and nascent.
In any case, if anyone wants to discuss further, I'd be very happy to share learnings. I'm gene@ the website I mentioned earlier. If anyone is Cambridge/Boston based and interested in the law sector, I'd love to get together!