Only Visa and Mastercard process Level 3 data. Amex only processes Level 2 but then has its own EDC format that includes similar data as Level 3. Discover doesn't participate at all. No idea about JCB.
Here's a very detailed technical explanation:
http://apps.cybersource.com/library/...III_SO_API.pdf
Merchants who participate generally pay lower fees to their payment gateway, so there's a big incentive to integrate with these programs.
(I lead a payments infrastructure team for a major tech company)