The big issue is cost. yes you can buy a SSD today thats 1TB but you'll spend $500-$1000 for it and I can buy a 1TB HDD for under $100. If the cost per size for SSD comes down to close to HDD then they can be replaced but you'll see them until then.

Things change. Floppy disks are still around, but are certainly obsolete for mainstream use. Tape is still around, but not in really widespread use. Eventually spinning magnetic drives will be obsolete, but it's not obvious how long it will take. Flash drives are fast and reliable, and have had data recovered from them after severe physical damage. That is likely to be the way things will go in the near term, but other technologies might replace them. Unfortunately, it is rather difficult to see very far into the future. It is easy enough to see into the past, but many people don't want to look.

Maybe HDDs won't get extinct, perhaps they just get better, faster and larger with time.

I currently use a 32DB SSD drive just for the OS and a HDD for my home partition.

I'd like to see mechanical drives die out altogether (archival storage aside). The noise, vibration and need to spin up make them a bad choice for mobile devices and even on a desktop they take up a lot more room than the equivalent in chips.
In the same way swapping is almost obsolete in mid to high end desktops I hope the HDD goes that way too.

How long can a desktop's HDD last?
After 5 years, do I need to buy a new HDD to backup my important data?

All your important data should be backed up as a matter of course anyhow -- off site if it's really important.
I've noticed that after 5 years or so hard drives do seem to have noticeably deteriorated and mine certainly seem noisier and are all showing SMART errors with the odd bad sector. Nothing terminal but enough that I'm replacing my drives at the moment.
Replacing my home drive with an SSD has meant Google Earth and second Life are a little quicker when using disk cache though for some reason Icedove and Firefox loading times haven't noticeably sped up.

Linux doesn't seem to react as positively to SSD's as the other OS's. This discussion was happening on OCN not long ago.

AFAIK
cycle life of SSDs is about 1/10,000th that of magnetic drives
used a swap space they will die in in less than an hour
magnetic drives will be around for at least the next decade or 2

Wow, the 300Gb one that's in my Windows desktop at work with 8Gb for swap that's been running pretty much 24/7 for 8 months must be a miracle! :) :) :)

Yea my now 4 year old vertex with 8GB of swap space is still going strong

Any studies?
My recollection of the "reliability" of magnetic drives is less than impressive. Of course, you can be lucky and they will last for far longer than their expected life but magnetic, spinny drives are no less falliablle than anyh other technology.

While I have had an excellent run with my HDDs only requiring replacement because they slowly become to small (apart from 1 back in the mid 1990s) I have not really heard that SDDs have the problem you have mentioned. I to would be interested in what studies you base this on.

For sure, all that laptops that only feature a SSD, not a mechanical drive, that come pre-installed with Windows, using the system partition to store the swap file died after an hour, without exception. Sorry, but do you have any link to a study that supports those claims?

To be honest, who knows for sure. They are still improving HDD speed and performance which is a sign they are not going away anytime soon.

Records are not completely extinct yet, they're still around, they're just not widely used as compact discs and digital mp3s. I believe HHDs will be like records in the future, still around but not extinct.