I am a new Amiga 'owner', as the only one I'd used previously belonged to my dad when I was very little. I don't remember much about it except for the games, and I bought an A500 recently purely for the sake of running some of them (Could have just used an emulator, but I like these things to be authentic ;-)). But as it turns out, once I got it I fell in love with the hardware instead! It's great fun pulling these old things apart, getting them looking like new, all the weird and wonderfull add-ons you can find.
So while not technically being new to the Amiga, I have come back to it for new reasons :-)