Firstly, are you overclocking anything? I ran a system overclocked for two years with no problems until I tried to run AOE III on it. AOE III doesn't like to run on overclocked systems.
Does the game crash in single-player mode? If not, then it may well be a connection issue. Over the years I've had crashes and freeze-ups that occurred when my ISP's bandwidth suddenly lowered or when too many were on the network. Make sure that the game is allowed full access and server rights through your firewall.
Random crashes to desktop are very hard to track down. If the crashes didn't occur when you first installed the game then a re-install and re-patch might be in order.
Before you do this there is some basic system maintenance you might perform: Run dxdiag and see if there are any errors reported. Also, a check for DirectX, Windows and video/audio/mouse/keyboard, etc. driver updates. A disk cleanup, temp file purge, defragmentation and complete virus scan wouldn't hurt anything either.
Some in-game option setting you might try:
- Set camera zoom to Near.
- Set Anti-alias Off (especially with an NVIDIA card).
Some versions of NVIDIA chipset drivers known to crash the game; you might try a chipset driver update if you have a NVIDIA chipset.
Also, over time some Windows files may become corrupted. If you right-click the Command Prompt icon in Accessories and run it as an administrator you can run the command sfc /scannow to check the integrity of your OS.
Check to see if there are any BIOS updates for your system too but be very careful to read closely to see if you actually need the update and be very sure that you follow instructions exactly -- failed BIOS updates can render your motherboard useless.
Here is an uninstall/reinstall procedure that has worked for Vista/Win 7 users. Of course, you won't have the disks but if the GFWL file has been saved to disk you can reinstall it from there, otherwise re-download the file. If re-downloading from GFWL it's best to open the Marketplace as an Administrator.
A last note: Over time, power supplies (especially the cheap low-wattage units installed in brand-name systems) can begin to fail and cause many seemingly unrelated errors.