You wouldn't be able to tell if someone else was reading your files - for example if you had some sensitive data.
I can't think of an OS level command that would need last accessed. Backups check last modified and date created for example. But see @mythokia's answer for one case that might.
Given that it's disabled by default in Windows 7 (thanks @AndrejaKo) and Vista that indicates that (unless there are other changes to compensate) it's OK to turn it off.
I've just thought of a reason why it might be disabled in the new OSes. These have the new Windows Search installed by default. This scans the selected directories for changes and re-indexes new and changed files. This would have written lots of events to the log which might be a reason for disabling it. There's more information on why they stopped updating the Last Access time from Vista onwards in MSDN blog post Why doesn't the file system have a function that tells you the number of files in a directory?.