Crashing for me too during character creation with the following message box: "Fatal Error: Error decompressing data." I've run the client multiple times and, after STO verified all the files, it crashed again the same way in the same place.
I have not been able to get past the character creation page, it crashes at different points.
It used to be quite stable at the start of the open beta. Then after the first weekend of the open beta there was a patch after which I could no longer play the game.
dxdiag says everything is okay:
Microsoft windows XP Home Edition (5.1, build 2600)
Default System BIOS
Intel(R) Core(TM)2 Duo CPU T9400 @ 2.53GHz (2 CPUs)
525MB used, 2108MB available
DirectX 9.0c (4.09.0000.0904)
I have tried the Screen/Sound and Music test in dxdiag which all succeeded.
I even uninstalled STO and reinstalled, it didn't help.