I am running a software RAID 1 in Windows 7 Ultimate x64.
Are there any tools in Windows 7 that can monitor or detect whether my RAID 1 is working properly?
If you go to Computer > Right-Click > Manage > Storage > Disk Management (where you probably came to create the software RAID) You should see the RAID status. Typically, it will be "Healthy", or can also be "Rebuilding" (array is still building after mirror creation, or disk replacement), "Failed RAID" (a disk has failed so replace it and theinformation is still avalible) or "Failed" (which is when you reach for your backups).
I don't know if there are any other built-in tools for Windows 7/2008 but this should be enough.
You could use the free (Open Source) WinRaidMonitor, which can inform you via Email as soon as your Windows software RAID is not healthy any more.