Forgive me if the following post is imposing! I just figured I'd throw little descriptions/recommendations up too in case anybody was interested, then it turned out kind of long.
Herbie Hancock has been mentioned already, but I'm going to add a little about him in the hopes it might spur somebody to check him that hasn't already. Basically, if you're at all into Jazz or want to be, missing him out would be like missing Coltrane. He has a back-catalogue of about 50 years and he's kind of crucial in Jazz. No one album is representative of his music but I recommend Maiden Voyage for that classic Jazz piano and for its reputation too I guess. I'd also recommend Head Hunters for the sheer comparison. It's straight Funk, Jazz Fusion, whatever and just proves what I said about no one album be wholly representative. If you've never listened to him before I think those are good places to start.
Robert Glasper is another pianist. You'd typically find him as a session musician for the likes of Mos Def and Talib Kweli, but he has his own records that are kind of like a contemporary answer to classic Jazz. He's an interesting case too because he sort of transcends the impression of both Jazz and Hip Hop. The album Double Booked is kind of celebration of that. For anybody now turning their face at the thought of Hip Hop, stop it. Hip Hop is good. And anyway, the music isn't really identifiably Hip Hop, but you can understand its sort of spiritual place within it. I'd recommend the album In My Element, probably because I love his adaptation of Herbie Hancock's 'Butterfly' (from Maiden Voyage, incidentally) mixed with Radiohead's 'Everything in Its Right Place'. Something to note on his albums is the drumming. It's nuts. I saw him live late last year and it was like a tennis match between the two. You look at one and you miss something cool that the other did.
Nostalgia 77 keep in the theme of Hip Hop influenced Jazz. When founded they were British, which is something new, and the nucleus of the group is a British dude. I'm told a certain British style comes through in their music but I don't think I'm informed enough to notice myself. They're sort of a shape-shifting collective and change style from album to album though, so it's possible it was only present temporarily, until a new style replaced it, and a new style replaced that. As far as instruments go, they have everything. Horns, bass and drums lead a lot. I can't really pin down what it is, but it sounds great. I think it's like if you mixed Soul and Funk with Jazz and left it instrumental. They are unique, and I think a lot of you would like them. Anyway, check out The Garden if you want. For people open to something more Hip Hop influenced, check out Songs For My Funeral.
Yesterday's New Quintet once more arises from a background in Hip Hop, or rather Madlib (every member of Y.N.Q.) arose in Hip Hop from a background of Jazz, Soul and Funk. It's hard to tell, but Yesterday's New Quintet are a sort of homage to everything about Jazz. Much of Y.N.Q.'s catalogue are tributes to idols of Madlib's in the form of covers, reinventions, emulations or adaptations, but they are certainly his own records. You know they're Madlib's when you hear them. My favourites are The Funky Side of Life, though that may be under the alias 'Sound Directions', and Angles Without Edges.
Medeski, Martin & Wood I'm surprised haven't come up. They tend to be one of the most frequently encountered names amongst Jazz listeners similar to my age (I'm 21). They're a standard Jazz trio: piano, double bass, percussion. They're sort of post-modern Jazz. Not quite Free Jazz, though they break into that half way through songs occasionally. If you like Weather Report you might like these; they're fusion-ish. Again, they never really stay in one musical spot for too long, and actually did a children's album, haha. I'd recommend It's a Jungle in Here.
Esbjörn Svensson Trio (or E.S.T.) are another significant group (piano, double bass, percussion), and represent a different point of entry into Jazz. They're Swedish, for one, and wave a flag for quite a large Jazz following coming from Europe that tends to be distinctly different in style and tone to its American counterpart. Other good examples are Tomasz Stanko, Tord Gustavsen and Marcin Wasilewski (Google gives you some Polish Football player; it's not him). Despite them all sounding different to each other there's like an overarching connection that identifies them as European. Anyway, E.S.T. are a sort of progressive Jazz group, but if you think of 'progressive' in its application to Rock music. They aren't experimental Jazz; it's as if they treat Jazz music with the sensibility of a progressive Rock musician. It's hard to explain, and I don't know if you'd get that from listening to them. It's just how I see them. Regardless, they're interesting. I really liked Viaticum if anybody feels like checking them out.
There! I mentioned all of these, well, because they're my favourites but I think if anybody entered this thread looking for diversity, they all reflect that but remain essentially Jazz. I could add Thelonious Monk and Fela Kuti, but ehhhh. This is long enough I think.
Also, @20thCenturyBoy Nicole Simone (unsure on a relation to Nina) has a nice eerie voice, and Nostalgia 77's Everything Under the Sun has a lot of Jazz singing on it. There's this girl that was the tour singer for Herbie Hancock when I saw him last year too; her name is Kristina Train. She's on Blue Note and worth a listen if you're into it.
Thanks for reading.