There's a great searchable database (two actually - US and "rest-of-the-world") of litigation here.
From the About page:
This website provides two databases of climate change litigation: (1) a U.S. Climate Change Litigation database and (2) a Global Climate Change Litigation database, which includes all cases except those in the U.S.
The U.S. Climate Change Litigation database is a joint project of the Sabin Center for Climate Change Law at Columbia Law School and Arnold & Porter. Michael B. Gerrard, then a partner at Arnold & Porter and now Faculty Director of the Sabin Center, and J. Cullen Howe, an environmental law specialist at Arnold & Porter, first created the U.S. Climate Litigation Chart in 2007. In 2017, it was relaunched as an interactive and searchable database. The U.S. chart is updated on a monthly basis, and currently includes 1621 cases* with links to 10550 case documents.
The Global Climate Change Litigation database was created in 2011 and is updated regularly. It currently includes 750 cases, with links to 1557 case documents. At present, the Global database features cases from over 55 countries. The database also includes climate litigation cases brought before international or regional courts or tribunals.
Edit: For example, here's a quick list of all 37 climate change cases involving Exxon.