I just recently bought myself a new computer, not just to play empire explicitly on, but I do play it on it, I also have Windows Vista 64bit and I do have these crashes to the desktop in battles and occaisonally the Campaign map.

I can only recommend one piece of advice so far that has lessened the crashes for me (before it was rediculous, now I'm lucky to get one crash every second battle -

Turn off Depth of Field, it helped for me slightly.

For those that are curious here is a complete list of Errors I have recieved:

Spoiler Alert, click show to read: 
Product
Empire: Total War

Problem
Stopped working

Status
Report Sent

Problem signature
Problem Event Name: APPCRASH
Application Name: Empire.exe
Application Version: 1.3.1.0
Application Timestamp: 4a4e5af1
Fault Module Name: MSVCR80.dll
Fault Module Version: 8.0.50727.4016
Fault Module Timestamp: 49cc5361
Exception Code: c0000005
Exception Offset: 0001500a
OS Version: 6.0.6002.2.2.0.768.3
Locale ID: 3081
Additional Information 1: fd00
Additional Information 2: ea6f5fe8924aaa756324d57f87834160
Additional Information 3: fd00
Additional Information 4: ea6f5fe8924aaa756324d57f87834160

Extra information about the problem
Bucket ID: 1357449786


Spoiler Alert, click show to read: 
Product
Empire: Total War

Problem
Stopped working

Status
Report Sent

Problem signature
Problem Event Name: APPCRASH
Application Name: Empire.exe
Application Version: 1.3.1.0
Application Timestamp: 4a4e5af1
Fault Module Name: Empire.exe
Fault Module Version: 1.3.1.0
Fault Module Timestamp: 4a4e5af1
Exception Code: c0000005
Exception Offset: 0045e9d1
OS Version: 6.0.6002.2.2.0.768.3
Locale ID: 3081
Additional Information 1: fd00
Additional Information 2: ea6f5fe8924aaa756324d57f87834160
Additional Information 3: fd00
Additional Information 4: ea6f5fe8924aaa756324d57f87834160

Extra information about the problem
Bucket ID: 1360520905


Actually nevermind about posting them all, that would get rediculous, Sufficed to say I have 11 of these reports so far. I saw one topic on a forum where one person has had 68! of these crashes, and as always the exception code is c0000005 and the fault module is either Empire.exe or MSVCR80.dll as far as I've been able to google no one has been able to figure it out, CA have not responded to the issue whatsoever as far as I've been able to ascertain and with no solutions, those of us who went out and bought brand new computers for this and high ended games, remain utterly annoyed by the fact that we have brand new computers which Empire can not run on properly! My old computer doesn't even get a crash on empire anymore, but here I am now wondering am I actually going to be able to finish my next battle? I hope someone figures it out soon!