My (personal!) suggestions, focusing on Single Player:

Stone Abyss - In the words of the author, a "scripted remake of the original JJ2 story": a fun, no-nonsense Single Player level pack that hews close to Epic's original levels while also greatly improving upon their design, effectively using JJ2+'s new features to add new challenges and effects.

Hero 4 Hire - The Final Adventures - If you simply want more vanilla Jazz Jackrabbit 2, but even better, this pack's got you covered.

The Demon Invasion - A short but sweet set of levels, which look great but are also very enjoyable to play. There's a story element as well, and as a whole the episode is a nice mix between traditional and innovative level design.

Tomb Rabbit 2 Unfinished - The sequel to one of the most popular custom level packs ever made for Jazz Jackrabbit 2. It's unfinished, but don't let that deter you - what's there is creative, challenging, and enormously fun, with custom graphics and music made especially for this release.

A Generic Single Player Level II - It's just one level, but it's big enough that it can entertain for hours. It's difficult but rewarding, and has a beautiful world for you to explore. Newer players will probably find it most enjoyable on easy mode, though you may also enjoy the challenge higher difficulties provide.

Episode Two: The Rebirth of Evil - If you're in for a challenge, give this one a try. This is probably the best installment of a huge, sprawling five-part series, famous for its creativity, ambition and punishing difficulty. Reaching the final level is enormously rewarding, but don't say we didn't warn you!

The Episode - Six levels that are a lot of fun on their own but perhaps especially interesting because they use four of the best user-made graphics sets available - showing to what extent the game can be customized. You can use Jazz Creation Station, the game's level editor, to easily make your own levels with these tilesets (or others! there are hundreds out there) too.