Is a UPS a good investment for a home machine?
Think of preventative equipment like UPS, RAID controllers, tape drives, etc. as insurance. If you're willing to risk the odds, then by all means don't get the equipment. Save a few bucks in the short term and pat yourself on the back. But like a car crash, if you value anything about the car, then insurance is worth it as life in and of itself is a gamble.
Weeks, months, maybe years from then, what do you think the odds of something going wrong? Multiply that by the amount of time needed to diagnose, repair, test whatever problem occurs.
If money is an issue, I can understand skimping here and there because of a lack of funds. But if money is fairly accessible and you consider your work/computer/data/files/whatever important, then not buying any preventative equipment is simply foolish.
To answer your questions directly:
Is it worth the money to invest in a battery-backed UPS unit for a home machine?
Do you consider your data valuable or not. If you do, then I would definitely spend the money. $140-$160 UPS goes more than a long way for a home computer. There are probably cheaper units that are just as effective. I'm not saying you have to spend that amount but there are a variety of brands available that might meet your needs.
Or is it a waste of money?
Prevention is seldom a waste of money. I've had numerous disks go bad in my lifetime. Then I tried software RAID. What a joke. I still had data loss. Then hardware RAID (no problems yet) and now NAS (network attached storage) with an attached UPS. I sleep very comfortably at night with well over 400GB of storage.
The purpose of the UPS would be to prevent a "meltdown" of the computer due to bad power in the area, i.e. it's toast(tm).
The general idea behind a UPS is uninteruppted power supply. If a brownout occurs, no problem. The UPS switches to the battery to supply clean power and switches back when the line is A-OK. You'd be amazed at how many brownouts/blackouts occur when you're at work or in the middle of the night. Make sure to use the software between the computer and the UPS to log issues that arise.
With the cost of some computers, the UPS approaches half the replacement cost of the machine, which is why I'm asking.
Equipment costs aside, paying $300 for a computer and paying $150 for a UPS is a meaningless comparison. Let's be clear, data is the most important thing about a computer. When you get right down to the core, the difference between one machine and another is mere perception. If you could care less about files, and all you do is browse the internet, email and play games, maybe a UPS is a bit overkill. But if you value your personal and historical (private) information, a UPS is but a small step towards preventing disaster.
I should note there is one caveat to a UPS: cloud storage. If you care about your document/pics/whatever, you could use something like dropbox or Amazon S3 storage to remotely backup your information leaving your home computer to chance. Granted, if you trust those providers and wave any thoughts about your privacy, then that's a free/cheap alternative to a UPS.
Yes, you should have one. One that is sufficient for a home computer should not be that expensive. Here's an example. Here's a quick article on some of the benefits. But, basically electrical power disturbances can cause hardware damage and even data loss.
I purchased an APC SmartUPS 1500 about 5 years ago as the electric here kept dropping out, I've had to replace the battery once since but it's been well worth every penny, and because the computer is fairly good on power now days it lasts for ages when the power does do off.
I've been very pleased on lots of occasions that I have it, you only need a really short power failure and all your unsaved work can be gone which is really painful (esp. if your doing a long video processing task or similar) – it's also reassuring to be able to carry on working and not worry about loosing unsaved work when theirs a thunder storm in the local area!
So in summary YES – but be careful with your purchase as I also have a cheep one (cost ca. £30) which is rubbish (you get what you pay for) – only just about up-to the job or powering my network switch.