I tend to be a very non-main-stream ttrpger. The last game of D&D I played was 3.0 back around 2000. D&D is, in my view, a system that does not greatly encourage role-playing, but does greatly encourage tactical thinking, and optimizing characters as either damage dealers or force multipliers (mostly via healing the damage dealers).
To expound on that thought, I tend to feel there are two important qualities to role-playing games: mechanics and universe/genre. Some games, of course, have no genre, and aim to be a generic system that can be used anywhere. Of those, the two I'm most familiar with are GURPS and HERO. Of those, I think GURPS is far better at less cinematic games and settings, while HERO does far better with the more cinematic ones. GURPS has a weaker characteristic system (4 stats, 6-14 is the approximate human range) than HERO (10 stats, 0-20 is the approximate human range), but a far chunkier (and, in my opinion, better) skill system. Both have similar systems for handling powers/spells, mostly consisting of base effect * positive modifiers to power/negative modifiers to power.
For diceless systems, I'm mainly familiar with Amber and Nobilis. Amber is less strongly tied to its universe than Nobilis, but both would take work to change the genre on. Of the two, I find Amber less interesting. While I enjoyed the Amber books, I don't find the universe one that really pulls me in as a character. The universe of Nobilis, on the other hand, with the players taking on roles that literally control a single aspect (usually) of reality, is more intriguing to me. I also find the mechanics that Nobilis put in place (one uses MP to power their superhuman abilities, including changing the nature of their aspect of reality, and gets MP back for roleplaying, mostly) far superior.
For fantasy role-playing, I've settled on a couple of favorites over the years. I tend to like my fantasy to be low fantasy, with a grittier, more simulationist style. Ars Magica has a fairly gritty setting, with several non-standard suggested practices. The magic system is also my favorite magic system ever: 5 verbs, 10 nouns, and effects are made up of one of each, with low power spontaneous effects being possible on the fly, or more powerful singular effects being able to be researched in down-time. It's based on 13th century Europe as it existed, but the system can be shifted to work in other areas where you want long-term characters with powerful magic.
I'm also a fan of Legend of the Five Rings, especially for groups that are more interested in playing roles that are less like modern Western tropes. The system is more complicated than D&D, but still toward the easier end of the scale, I think, as it has pseudo levels and classes. It really shines in its setting, which is well fleshed out, and its genre elements, which have decent mechanics for groups that have problems handling them just through role-play.