For me it was probably because as kids you always tend to support the underdogs and Zimbabwe were the team you always loved watching win over the bigger guns during the 90s and early 00s, so for me it was very sad to see them go down the way they did, in addition to that I was a fan of Andy Flower and Heath Streak, Andy in particular was an unbelievably good cricketer.
One common thing will also be that Zimbabwean players have always been humble, I don't remember a single instance of them being arrogant or abusive, they are like the ones who just can't hate! So naturally we started liking them.
And Googly, I don't think you need to have ties, I mean I was a die hard fan of Andre Agassi and I'm not his relative nor have anything to do with USA
I've been a huge huge fan of Wasim Akram too, as a kid I started watching cricket because of him and Sachin, and he is a Pakistani... But for me sports never sees any boundaries.