I've had four computers on which Word crashes for lack of memory, but Microsoft doesn't publish the memory requirements for Word.
Microsoft gives general memory requirements for Office (and for the individual applications if you buy them separately). For example, Office 2003 says "128 MB of RAM or above recommended," and Office XP gives a requirement for each supported OS (128 MB for Windows XP, 64 MB for Windows 2000 Professional, 32 MB for Windows Me or Windows NT, or 24 MB for Windows 98), plus 8 MB for each application running simultaneously.
These miserly recommendations will give wretched performance, because they're barely enough for the operating system itself to work welland Word needs plenty of RAM on top of that. A typical Word 2003 session with a couple of documents open often takes 50 MB of RAM and 25 MB of virtual memory. Word XP is a bit less greedy for RAM than Word 2003, and Word 2000 much less so. But if you want Word to run without problems, make sure your PC has more than enough RAM. If you're running Windows XP or Windows 2000, consider 256 MB the bare minimum for using Word.
To check on memory:
If you're not sure how much memory your computer has, right-click My Computer and choose Properties (or press Windows Key+Break) to display the System Properties dialog box. Check the Computer readout on the General tab.
To check how much memory is in use, right-click a blank space in the taskbar or notification area and choose Task Manager; then click the Performance tab and look at the Total readout and the Available readout in the Physical Memory area. These numbers are in kilobytes; divide by 1,024 to get the number of megabytes.
To check how much memory Word is using, click the Processes tab, find WINWORD.EXE in the Image Name column, and look at the Mem Usage column. That's the amount of RAM. To see the amount of virtual memory, choose View » Select Columns, check the Virtual Memory Size box, and click the OK button. You may need to resize the Windows Task Manager window to display the VM Size column.