Did you try another USB port (the front ports are treated as a seperate device than the back ports - if you've been using it in the front, try putting it in the back - maybe the front ports went dead).
When you plug it in, do you see a "Safely remove hardware" icon appear on the taskbar by the clock? If so, open it and see is if a "USB Mass Storage Device" is listed. When you unplug the stick, it should disappear from the list.
If it appeared in there then plug the stick back in and right click My Computer, select Manage, open Disk Management. The stick should be listed at the lower right of the window. If it doesn't have a letter assigned to it, right click on it and assign it a drive letter.
If it doesn't appear in there then open Device Manager (while the stick is still plugged in) and see if there's a device with a yellow exclamation (might be a USB device, a disk drive, or an "Other" device). If so, right click on it and uninstall it. Pull the memory stick and then plug it back in and hopefully it'll recognize it.
I assume this is XP? Did this start happening recently? Worse case use system restore to roll your computer back to a restore point prior to the problem occuring. Remember that any files outside the My Documents folder will also revert to the condition they were in on that day. This is reversible - you can always restore back to where you started.
Hope this helps...