It's still possible to fly on the jumpseat with some airlines outside of Europe/USA, last year I managed a couple of jumpseat flights on the A320 in Asia by showing my PPL and thoroughly enjoyed them.
As for service, I enjoy Qantas, Cathay, Asiana and Etihad (ish/mostly). Whilst I fly a mix of business and economy, the best flights are always the opups, just a real feeling of being lucky.
One of my most memorable flights was a Virgin one across to Miami in Premium Economy last year, was kind of a different experience as it felt much like a charter holiday trip, rather then the normal glum faces (mine included) deep in thought about work.