Here's an interesting try for an advantage against the Najdorf:
6. Be3 e5 7. Nde2!? I've just found it by accident in the Shredder database. It scores >67% from 23 games with players of >2500 ELO, but this is probably primarily because it's a recent development. I don't think it's objectively stronger than main line. Still, it can't be ignored because Nisipeanu and several other strong GMs have been been playing it with fantastic success against tough opposition.
It seems that Nde2 is very flexible and perhaps more useful move in trying to prove that Black's d5 and f5 holes are weaknesses. Nde2 often goes to g3 (against Be7 and Nbd7) from where it can go to f5 and basically force Black to play Bxf5, thus weakening d5. Moreover, Nde2 can also support an immediate Nd5 with Nec3, giving White a d5 stronghold. It's also interesting that it supports f4. Thus, Be6 can be well-met by f4-f5 and if Black isn't careful, White can get a dangerous attack. Also, it is important that Black's queenside play is in many ways rendered ineffectual because the b5-b4 advance no longer kicks the knight on b3 and White doesn't generally plan long castle. White's better central control can also be used to diffuse much of Black's counterplay. It is really a very clever move with some deep ideas attacking the very heart of the Najdorf, the d5 square (and to a lesser extent f5).
Since, natural developing moves seem to do very poorly for Black, the best try might be Ng4. The knight blocks e2, the queen cannot defend f2 and thus, Qb6 is very strong if White tries to move the bishop out of the way. Thus, Black is at least guaranteed the the bishop pair as compensation for his structural weakness. However, this might prove to be a temporary trump because he might have to exchange the light square bishop for a knight on d5 or f5 and the dark squared bishop might be captured by the d5 knight, or even exchanged for the supporting e3 knight to improve d5 control.
Here is a possible variation: ... 6. Be3 e5 7. Nde2!? Ng4 8. Nd5 (Ng3 and the meek Qd2 are alternatives) Nxe3 9. Nxe3 (other moves give White doubled pawns, which Black can attack with g6 and Bh6) Be6 10. Nc3 Be7 11. Ncd5 (Bc4 is also interesting)
Black to move
After this, I'm not sure how Black or White should play (Nde2 has very little theory), but play could continue 11. ...Bg5 (or 0-0 or Nbd7) 12. Be2 0-0 13. 0-0 Nd7 14. c4 Rc8 15. Nf5 Bxf5 16. exf5 Nf6/Nb6 with a positional bind type of position and an apparently small edge for White. Suggestions and/or analysis is very welcome.
I'm really curious about what you all think of this new idea! It's very interesting, relatively unknown and difficult to play against. There is great scope for creativity and improvement for both sides. Maybe some time in the future, this will be an alternate main line or at least popular outside of a small circle of strong GMs. The Najdorf seems to change every time I look at it, but it never loses its appeal and excitement.
Here are some example games of GM Nisipeanu with decent play from both sides:
http://www.chessgames.com/perl/chessgame?gid=1404531 1/2 - 1/2
http://www.chessgames.com/perl/chessgame?gid=1436773 1/2 - 1/2
http://www.chessgames.com/perl/chessgame?gid=1418820 1 - 0
http://www.chessgames.com/perl/chessgame?gid=1415018 1 - 0
http://www.chessgames.com/perl/chessgame?gid=1456750 1 - 0
http://www.chessgames.com/perl/chessgame?gid=1419017 1 - 0