I don't really go for the whole functional model, but as an INTP I answered that I enjoyed it as an Fe user (I believe that's the prevailing functional choice, anyway).
I wasn't completely crazy about it (I wouldn't put it in my "all time favorite shows list") -- I originally started watching it at the beginning of the first season when I thought it was legitimately about people who were stranded on an island and needed to work together to survive the elements (sort of like a group version of Cast Away). So I was a little nonplussed when the polar bear came chugging out of the jungle .
So I didn't watch it religiously or anything, but if I was around and not doing something else I'd turn it on and keep track of it, more or less. Which means that I probably watched 80-90% of the episodes, especially in the last season or two when I had easy DVR'ing available.
Why did I enjoy it? I think that in general it had intriguing (if not altogether coherent) storylines, a fair number of characters that I really liked (Hurley, Sun, Jin, Juliet, Sawyer, Vincent (of course!) and even Jack and Kate... sometimes), some great acting (Michael Emerson as Ben and Terry O'Quinn as Locke, particularly) and a certain endearing craziness. And some pretty great Hawaiian scenery.
In the end, I tend to like long, involved, complex stories that I can put myself into a sort of "if I was there, what I'd do / adventurer" mode. Lost, while weird and practically unfathomable at times, fit that bill pretty well.