Windows 98 SE shutdown problems

I've found that to be the most common reason for shutdown hangs is IPX protocol trying to find the network (to say goodbye or something). As long as it's on the network it's fine. Beyond that, you didn't even mention what kind of shutdown problem you are having.
Remember back to when the problem started happening, and try to remember what change you made to your system (new hardware or software, changed a setting for your sound card, updated driver, etc) and undo it, and see what happens.
Otherwise, post a little more info on the system and the kind of shutdown problem you're having.

With 98 are related to networking or network drivers as far as my experience of shutdown problems goes. I have seen dozens of machines that start up, work and shut down just fine UNTIL they are used to access the internet or connect to another machine on a network. Simply using dial up networking to establish a connection and then disconnecting without even launching a browser or mail program can cause a system to hang on shutdown. My first thought is to remove all network adaptors, protocols and services and then re-install them. The go to the Microsoft site for the updates for Mapped Drive shutdown and Drive Caching supplement...this will often cure the problem. Failing that search for information on shutdown problems and troubleshootingon the MS KnowledgeBase.