Freedom Planet is heavily inspired by the early Sonic games. It's very good too.
Giana Sisters is somewhat Sonic-like (despite its original being an outright Mario Bros clone/rip-off on the C64 - swiftly withdrawn from sale). A tough challenge too, in later levels.
As mentioned, Darksiders is very Zelda-like, mechanically. Even has a hook-shot.
If you ever played Earthbound back in the day, which was a great JRPG, then LISA is similar.
Volgarr the Viking is a Ghouls & Ghosts / Rastan type game, is tough as nails, and is my outright favourite game of the past 8 or so years
The 2014 Gauntlet game is a modern version of the classic arcade game, rather than a game in the style of the original, but I found it pushed the right buttons.