I've been in the same foreign country (Korea) for going on 6 years, so my answer to this question has changed.
Originally what I loved most about being here was the exploring: downtown shops, restaurants, temples and just regular streets. Now that those things aren't new to me any more I notice the unpleasant parts that never bothered me before: the traffic and the crowds, mainly.
But something keeps me here and keeps me interested. After 6 years I still don't understand how things work or why people do things the way they do, I guess I mean the culture. And I have yet to learn enough of the Korean language (I do intend to) which is key to understanding the culture from within.
Maybe my favorite thing about living abroad, though, is that this lifestyle is not at all possible in Canada (where I'm from). Having take-out food delivered to my door and then setting the dishes back outside for them to pick up, for example. Living comfortably (with money to spare for eating in restaurants every day, if need be) with working hours under 20 per week.
I'm sure I'll think of more answers, if not my absolute favorite thing about living abroad. These are my musings for today.