The best edition of the State Trials is that by Cobbett and Howell. Links to the all 33 volumes on Google have been diligently compiled by Naomi Clifford. Another set is hosted by the Constitution Society.
A preceding compilation, ‘A Complete Collection of State-Trials, and Proceedings For High-Treason‘, (6 volumes, 3rd edition, 1742) is also hosted by the Constitution Society, in chunked pdfs of 50 pages each. The Internet Archive has this set, with the four additional volumes, the last published in 1766. The second edition (6 vols, 1730) of this can be found on Hathi Trust.
Wikipedia has links to the Internet Archive’s copies of the 8 volumes of the State Trials New Series.