Good question (the original thread). I have given it quite a bit of thought lately.
I have seen some answers I can relate to, but I am not in it to brag. My lovestick isn't bigger (or feels) bigger because of the Amiga's I own. At all actually.
My idea was that, at some day, I would like to open a museum. The time isn't right yet though, maybe in ten years time. I do not just collect for myself, I also like to spread the word, and help out with knowledge I have. And yes, some of that is built up by owning stuff. I did make a website 'to show it all off', but it didn't start out like that. One day I hope to make a site much like the Amiga Hardware Database, and share my collection of original driver disks, the rom files from cards I own etc.
Yes, some might despise people that collect, or look down on us, merely because we can't program code. But keeping these machines alive, intact, running and in good condition is hard work in itself. No car runs without a mechanic. I will help out people, and therefore the community as a whole benefits. Example: little while ago I helped someone out that had an old PAR hard drive with personal work on it. I recorded it on DVD for them, because I can and because I own a working PAR machine.
At special events I often take along special or rare machines (most collectors won't, being to afraid of damaging it), and not to show off but to make people familiar with a part of computing (or Amiga) history they never heard or seen before. It's not meant to be hidden in my attic, I actively invite anyone to come over for a cup of coffee (pun intended) and remember the good old days.