With the Internet existing, I don't think anything really counts as obscure, especially among enthusiasts like us. So when I hear the word "obscure," I just take it to mean the least popular thing that we can think of, which usually relates to its sales.
I never owned a Sega 32X but I did know a friend who had one, and the first time I played DooM was on it. Probably a good thing I didn't know how much better the PC version was, as at the time it seemed like such an amazing game.
When Sega was exiting the console business and the Dreamcast was discounted to like $30-50, I wanted to buy one, but couldn't find one. I guess people bought 'em up fast at that price, hee hee. That was the closest I've come to wanting an "obscure" system, or at least one that wasn't on the market for long. Probably a good thing I didn't get it, as I don't think most of its games appeal to me, and some of its games I could get on GameCube like Sonic Adventure, Crazy Taxi, etc.