I'm having a similar issue as Eric Wilde; I'll start the game, create a new game, and sometimes get as far as completing a couple of turns before the game crashes and Windows starts generating an error report.  I've updated my video card drivers, and if it's helpful here's a link to some of the error files that windows generates. 
Link
Link
Contents of the debug.err the last time I ran it:
Debug Message:  Version v1.0 Digital: Bonus Pack last updated on: Mon Feb 20 19:04:13 2006
Debug Message:  Could not find a TGN Serial No.
Debug Message:  *********DXDiag info follows.*********
System Info
Time: 2/21/2006, 15:57:45
DirectX Version: DirectX 9.0c (4.09.0000.0904)
Machine Name: GHOSTPLANET
Operating System: Windows XP Professional (5.1, Build 2600) Service Pack 2 (2600.xpsp_sp2_gdr.050301-1519)
Languages: English (Regional Setting: English)
System Manufacturer: MSI                             
System Model: MS-6380E                        
BIOS: Version 1.00                    
Processor: AMD Athlon(tm) XP 1800+,  MMX,  3DNow, ~1.5GHz
Physical Memory: 512MB RAM
Page File: 456MB used, 536MB available
Windows Dir: C:\WINDOWS
Display Info
Display device 1:
Device Name: \\.\DISPLAY1
Card Name: RADEON 9600 SERIES
Manufacturer: ATI Technologies Inc.
Chip Type: ATI RADEON 9600 Series AGP (0x4152)
DAC Type: Internal DAC(400MHz)
Key Device: Enum\PCI\VEN_1002&DEV_4152&SUBSYS_00021002&REV_00
Display Memory: 128.0 MB
Current Display Mode: 1280 x 1024 (32 bit) (60Hz)
Monitor Name: SONY SDM-X82 DVI 
Monitor Max Resolution: 1280,1024
Driver Name: ati2dvag.dll
Driver Version: 6.14.0010.6599
Driver Date: 1/24/2006 19:52:48
DirectX Acceleration Enabled: Yes
 
Sound info
Sound device 1:
Description: SB Live! Wave Device
Default Sound Playback: Yes
Default Voice Playback: Yes
Hardware ID: PCI\VEN_1102&DEV_0002&SUBSYS_00201102&REV_04
Manufacturer ID: 1
Product ID: 100
Driver Name: emu10k1m.sys
Provider: Microsoft
Driver Version: 5.12.0001.3300
Driver Date: 8/17/2001 11:19:26
Type: WDM
Other Drivers: 
Acceleration Level: 3
Cap Flags: 0
Min/Max Sample Rate: 0, 0
 
Debug Message:  *********END dxdiag info.*********
Debug Message:  Entering WinMain
Debug Message:  ******* Starting Game Shell *******
Debug Message:  Preparing to change display settings.
Debug Message:  Using multilsample setting: D3DMULTISAMPLE_NONE
Debug Message:  Game Resolution: 1024 x 768
Debug Message:  Running in windowed mode.
Debug Message:  HAL (hw vp): RADEON 9600 SERIES
Debug Message:  D3DPRESENT_INTERVAL_IMMEDIATE
Debug Message:  Refresh rate: 0
Debug Message:  Bit Depth: 32 bit.
Debug Message:  *********Checking D3DDevice Caps***********************
Debug Message:  A full-color cursor is supported in hardware at high resolution modes.
Debug Message:  Border size reported as 6 by 25
Debug Message:  RGB in format 6:6:6, Masks reported as ff0000:ff00:ff
Debug Message:  Now windowed.
Debug Message:  Shell initialization complete
Debug Message:  ***** Initializing Game *****
Debug Message:  Timer Frequency is 0 369e99
Debug Message:  Initializing sound card.
Debug Message:  initailizing bink
Debug Message:  Create setup screens.
Debug Message:  Clear galaxy settings.
Debug Message:  Clear influence.
Debug Message:  Clear up laws.
Debug Message:  Clear first time events.
Debug Message:  Clear wonders and trade goods.
Debug Message:  Clear sector mapper.
Debug Message:  Set mouse.
Debug Message:  Set update timer.
Debug Message:  Clear data definitions.
Debug Message:  No files found matching mask C:\Documents and Settings\Steven\My Documents\My Games\GalCiv2\*.StarSystems
*DEBUG ERROR: ***Unable to find required tech ImpossibleTech for PirateShip. ***
*DEBUG ERROR: ***Unable to find required tech ImpossibleTech for Starbase. ***
Debug Message:  No files found matching mask C:\Documents and Settings\Steven\My Documents\My Games\GalCiv2\ships\*.shipclass
Debug Message:  No files found matching mask C:\Documents and Settings\Steven\My Documents\My Games\GalCiv2\ships\*.shipcfg
Debug Message:  Reading Star Names
Debug Message:  Reading Star Names... Done
Debug Message:  CustomRaceWnd: Cannot find OBJID CustomRace_Description_Text
Debug Message:  CustomRaceWnd: Cannot find OBJID CustomRace_Tab_Homeworld
Debug Message:  Creating Galaxy
Debug Message:  Set galaxy size.
Debug Message:  Killing threads.
Debug Message:  Kiling civs.
Debug Message:  Killing ships.
Debug Message:  Killing rallypoints.
Debug Message:  Killing misc objects.
Debug Message:  Killing stars.
Debug Message:  Killing anomalies.
Debug Message:  Killing space resources.
Debug Message:  Killing colonies and planets.
Debug Message:  killing scenario.
Debug Message:  Clear galaxy settings.
Debug Message:  Clear influence.
Debug Message:  Clear up laws.
Debug Message:  Clear first time events.
Debug Message:  Clear wonders and trade goods.
Debug Message:  Clear sector mapper.
Debug Message:  Creating Random Map
Debug Message:  Creating Random Map... Stars
Debug Message:  Number of Unplaced Stars: 4.
Debug Message:  Creating Random Map... Planets
Debug Message:  Creating Random Map... Anomalies
Debug Message:  Num Anomalies: 42
Debug Message:  Creating Random Map... Resources
Debug Message:  Creating Random Map... Done
Debug Message:  Creating Civs
Debug Message:  Terran Alliance: Intellence -> 30
Debug Message:  Drengin Empire: Intellence -> 30
Debug Message:  Altarian Republic: Intellence -> 30
Debug Message:  Torian Confederation: Intellence -> 30
Debug Message:  Yor Collective: Intellence -> 30
Debug Message:  Creating Civs... Done
Debug Message:  Updating ZOC.
Debug Message:  Updating ZOC.
Debug Message:  Galaxy Create... Done
Debug Message:  UIBeginGame called with g_ulLocalPlayerID = 3
Debug Message:   setting size 16 x 0
Debug Message:   setting size 16 x 0
Debug Message:   setting size 16 x 0
Thanks in advance for any help.
Steve