I am alive with a Penium lll, running Windows Me with 128 Ram and 41% system resources free and it seems to work fine-ish.
Am I missing something in the computer world?
Why am I told that I need to junk this paper weight, buy a new computer with newer OS?
Economics.
It depends on what you use the computer for - if you want to keep on doing the same sort of stuff as everybody else, there will come a time when you have to upgrade - because some document will arrive that you can’t open (and the application won’t be supported in Windows ME), or some website you visit will demand browser capability not available for your platform, or you’ll buy a game and it will demand a minimum system spec that exceeds yours.
Some, all or none of those points may already have passed, or they may be just about to come.
Or it may be that your individual pattern of usage is modest and static enough not to run you into any significant obsolescence.
You probably ask this having not used a faster one at work. Your’s would be intolerable slow if you used a modern one. There’s nothing better to get someone to hate there old one, then to use a fast one at their job and come home to what used to seem fast at home.
If you can’t see a reason to upgrade, then why worry about it. If your worrying about it, you’re mot totally satisfied.
One good reason is that MS stopped supporting ME two years ago. There haven’t been any security updates for it since.
Define fine-ish. If you don’t have any problems or frustrations with it, congratulations, you’re doing better than I am with my 3 modern machines 
To enlarge on yoyodynes point, older versions of windows were notoriously easy to compromise, so if you’re proposing to stick with a WinME (barf!) system you really should have some additional security bolted onto it.
Really, it depends on what you want to do. I don’t see any reason that shouldn’t be fine for word processing, web browsing, spreadsheets and other things.
If you want to edit MPEG movies, work with very large/detailed databases (such as GIS mapping programs), or play fancy new games, you’ll need something stronger.
Of course, microsoft programs (including operating systems) always expand their resources to cutting-edge current machines, so you’ll be out of luck trying to run Vista or the latest Office or anything.
It’s not just MS that no longer supports WinME. Most firewall and anti-virus software doesn’t either (and the few that do will stop at some point), so as time goes by, you will be in ever-increasing risk of infection.
I’ll agree with the consensus. If you just want to play Solitaire, write your novel, send email, and browse the web, you don’t need anything different. Just make sure you’ve got your novel backed-up, because your security is outdated, and you might have to reinstall your operating system every so often.
But you’re not going to be able to play Quake VII, and so on. But you obviously don’t care about that, because your machine and OS wouldn’t play any games released this century, and you’d have already noticed this. So that doesn’t matter.
Eventually the hardware on your machine is going to fail, and you’ll have to buy a new machine, and that new machine is going to have a different flavor if Windows on it, and it will take you some time to figure out. But if all you still want to do is play Solitaire, write your novel, send email and browse the web, once you figure that out on the new OS you’ll be fine, and you can keep that new machine for another 10 years.
True, although as time goes by, you’ll become a somewhat less likely target through obscurity.
You always have your backup pencil anyway…