Should I throw away mid 2011 iMac?

if it suits your needs there is no reason to, if you experience issues with browsering being too old then firefx and other non chrome and edge browsers run on older macOS versions with newer versions browsers

Throwing it away is quite harsh. However, you need to accept the fact that is 14 years old at this point and doing things on it is only going to get more difficult.

Browser's are just the tip of the iceberg here.

You can sell it on eBay, donate it to Goodwill, etc...

You don't even need to buy a brand new Mac if you don't want to, but updating to a slightly newer model is not unreasonable at this point.

JR wrote:

I have a mid 2011 21" iMac with 8MB of ram and High Sierra (10.13.6) which works fine for my modest needs but once in a while I hit some problem (usually concerning browsers) and troubleshooting always leads to me being told that this computer and OS is "too old" and "obsolete" and "no longer supported" and my life will be ruined if I don't throw it away and buy a new one. I would like you all to give me your opinions about what I should do.

Old High Sierra Safari might not access new websites so use some other browser. For example the last version of Firefox for Sierra, High Sierra, and Mojave is Firefox 115 ESR so try that.

Firefox 115.0esr.dmg

If it still works and meets your needs, there is no reason to throw it away.

If it doesn't meet all of your needs, but there is something that it can do that modern Macs cannot (e.g., run 32-bit games; import digital video from MiniDV and Digital8 camcorders), you could consider getting a newer system, but keeping it around for the jobs that the newer system could not handle.

No don’t throw it out please.

I can well understand why you don’t want to create more landfill.

I have several such macs in working order with later OSs

I advice you to seek out your local apple user group where you can get advice in person on how to keep your mac

running longer.