Looking for new genres...

Punk rock despite being nowdays already too trivial and traditional has a unique blends with other styles if applied with contemporary literacy:
How'bout Country Punk?
Positively I'd define the genre that is performed by "Frigg a go-go" band.
Jazz Punk is more famous and can be represented by more bands such as "Lounge Lizards", "Curlew", "Pere Ubu"(previousely playing at more traditional punk rock)... George Cartwright from Curlew had made his few solo albums in similar style.
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Jazz derivatives and some examples
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Jazz have lots of different directions and styles but I wouldn't define anything well-known such as Jazz-Funk or Fussion...

Art-Jazz
I'd define something beyond improvisation - more close to the organized composition or opus that definitely may have all neccessary division of a classical composition such as prologue, development, coda or whichever applies. The composers and musicians that represent this genre are Phillip Johnston and Lindsay Cooper as far as my knowlege goes.

Progressive Jazz
I'd define as a blend of Fussion, Ambient and Funk together in one where musicians, composers although represent the same style but seem totally different from each other. I still can't distinguish Charlie Parker from Gerry Mulligan or Artie Show from Harry James because they represent the same style and play alike. That isn't the case with Progressive Jazz that had been evolved throughout years of musical development... The representatives of such style are too many but few of them are David Sylvian, Ruichi Sakamoto, Fish for Fish, Arsenal(Russia).

Try some "world music" or modern classical. In the category of "world music", if you like vocal music, you might try flamenco (try El Cameron), Fado (Mariza, or A. Rodriguez), or some of the work by Portuguese group Madredeus. You might try also some African music (try South African "Iscathamiya" (sp?) music, and Mbalax from Senegal (Youssou N'Dour is the most famous practitioner)). You could also try Algerian Rai music or other north African music. I don't much care for the pop-ish aspect of much Rai music but it's worth a listen to learn about it. If you haven't had much exposure to tango music, I would suggest you give it a try - I love it and think it is addictive. Cuban music has gotten more exposure since Buena Vista Social Club but not many people have dig much deeper and there is a lot there if you like the genre. Other things Ry Cooder (who helped bring BVSC to market) has delved into are also worth a listen (try Vishwa Mohan Bhatt's guitar/sitar-like Indian 'classical' music).

Otherwise, if you haven't and are so inclined, you could also try "modern" classical music such as works by John Rutter, John Tavener, Arvo Part, Philip Glass, or John Williams. I happen to be a big fan of Arvo Part and Tavener.

Dmitrydr-I would doubt you could even exhaust the genres you like.
Try reading related music magazines on the genres you like,you are bound to find new artists both similar and different to ones you like.
Try www.allmusic.com this is a great website because it always has related artists and descriptions of musical genres and sub-genres.
Related to what T bone mentions you could try Ambient music with great musicians like pianist Harold Budd or indeed the Eno classics.
Your descriptions are a little vague-have you tried Jan Garbarek who is pretty hard to catergorise due to the different types of music he's produced.
As such as much as some Audiogoners can help you really need to do the ground work yourself as only you know what you've heard and how far you are willing to test your tastes.
Good luck.

Thanks guys, great recommendations. I'm quite familiar with World music, especially with its Celtic stream, didn't listed it assuming it's a subclass of Folk. I guess I'm looking for kind of 'upgraded' world music, something like Peter Gabriel's 'Passion', with high level of emotional and structural complexity...
Neoclassics is new for me, and I really liked John Tavener, Arvo Part, have to try others yet. Just curious how good is the last Tavener's CD from RR? And, in general, which their CDs to start from?

I like Tavener's "Thunder Entered Her."