I am going to add my view (repeat: view) on this subject:
I recognise that different people have differing opinions on the subject. In my life experience, EVERYTHING has both pros and cons. Looking at the pros and cons, I do not see either action (replace or don't replace) as 'best practice'.
My experience is like that of maxtherabbit. To quote myself from [
here], "
My own experience is that the failure rate is relatively high if the tantalum capacitor has been unpowered for many years (e.g. I buy an 'unknown working status' motherboard from eBay), but the failure rate is very low for a tantalum capacitor that is periodically powered (e.g. I use my IBM 51xx computers at least every few months.)" I cannot remember the last time I replaced a failed tantalum (but I seem to remember it was on a Tandon floppy drive). The failure rate that I observe just does not justify my time in replacing all tantalum capcitors. That's just me. I do know that if I was to buy a 'I found this IBM PC in the attic' machine, I expect one or more tantalums to fail, over the course of say, the first 10 hours of operation. Then stability. It doesn't mean that another tantalum won't fail down the track, but it is very rare, and I attribute that to the fact that I run my 51xx computers (now down to 7 of them) at least every few months (for a minimum of an hour).
But that's my attribution, and if it's correct, I recognise that not everyone runs their computers as often as I do.
As for exploding components, as VERAULT brought to our attention, other component types can explode as well. And is there a reason why a new tantalum won't explode? My suggestion: Wear safety glasses when your computer is open.
I have military soldering skills. On the opposite end of the spectrum, there are people here with nil or poor or extremely poor soldering skills. It scares me to think of the damage that they could do to a printed circuit board. Those people should keep their soldering to a minimum, until their skill becomes at least adequate for the task (or find someone else to do the soldering).