Professional match where neither player castles? Are there any professional matches from serious players where neither player castles during the course of the game?
It won't be terribly common, but it's not unheard of either. Here are a few examples involving well-known grandmasters:

Ivanchuk-Csom (1989):

[fen ""]
[Event "Yerevan"]
[Site "Yerevan"]
[Date "1989.??.??"]
[EventDate "?"]
[Round "?"]
[Result "1-0"]
[White "Vassily Ivanchuk"]
[Black "Istvan Csom"]
[ECO "E20"]
[WhiteElo "?"]
[BlackElo "?"]
[PlyCount "49"]

1.d4 Nf6 2.c4 e6 3.Nc3 Bb4 4.f3 c5 5.d5 Bxc3+ 6.bxc3 Nh5 7.g3
f5 8.e4 f4 9.dxe6 fxg3 10.Qd5 g2 11.Qxh5+ g6 12.Qe5 Qh4+
13.Ke2 gxh1=Q 14.Qxh8+ Ke7 15.Qg7+ Kxe6 16.Bh3+ Kd6 17.Qf8+
Kc7 18.Bf4+ Qxf4 19.Qxf4+ d6 20.Rd1 Nc6 21.Qxd6+ Kb6 22.Qg3 h5
23.Bxc8 Rxc8 24.Nh3 h4 25.Qf2 1-0


Sutovsky-Morozevich (1998):

[fen ""]
[Event "Pamplona International"]
[Site "Pamplona ESP"]
[Date "1998.12.31"]
[EventDate "?"]
[Round "05"]
[Result "0-1"]
[White "Emil Sutovsky"]
[Black "Alexander Morozevich"]
[ECO "C11"]
[WhiteElo "2575"]
[BlackElo "2625"]
[PlyCount "52"]

1. e4 e6 2. d4 d5 3. Nc3 Nf6 4. Bg5 dxe4 5. Nxe4 Be7 6. Bxf6
gxf6 7. Nf3 a6 8. Qd2 b5 9. Qh6 Bb7 10. Bd3 Nd7 11. Ng3 f5
12. Nh5 Bf8 13. Qe3 Nf6 14. Qe5 Nxh5 15. Qxh8 Bxf3 16. gxf3
Nf6 17. Rg1 Qxd4 18. Rg8 Ke7 19. Kf1 Bg7 20. Qxg7 Rxg8 21. Qh6
Qxb2 22. Re1 Qc3 23. Qh4 c5 24. Rd1 c4 25. Bxf5 Qxf3 26. Qd4
Nd5 0-1


Andreikin-Jumabayev (2009):

[fen ""]
[Event "48th World Junior Championship"]
[Site "Puerto Madryn ARG"]
[Date "2009.10.31"]
[EventDate "2009.10.22"]
[Round "10"]
[Result "1-0"]
[White "Dmitry Andreikin"]
[Black "Rinat Jumabayev"]
[ECO "E38"]
[WhiteElo "2659"]
[BlackElo "2548"]
[PlyCount "41"]

1. d4 Nf6 2. c4 e6 3. Nc3 Bb4 4. Qc2 c5 5. dxc5 Bxc5 6. Nf3
Qb6 7. e3 Qc7 8. g4 h6 9. Rg1 b6 10. g5 hxg5 11. Nb5 Qd8
12. Nxg5 Bf8 13. c5 Rh5 14. Nd6+ Bxd6 15. cxd6 Bb7 16. Nxf7
Be4 17. Qxe4 Nxe4 18. Nxd8 Kxd8 19. Bg2 Rg5 20. Kf1 Rxg2
21. Kxg2 1-0