They do happen - but only pre-arranged like international call-ups (for which the system doesn't work properly for anyway - 3 international call ups should mean postponement), never turn up for a game and it's been called off due to waterlogged/frozen pitch etc.
Definitely needs to happen a lot more often. Postponements midway through matches too. Happens in real life, hence - should happen in FM.
In a way, I'd like it but in another way I wouldn't. Imagine if you were in the last minute of the Champions League Final and you were ahead and then the match gets abandoned, how would you feel? I also imagine it would cause loads more "the AI cheats" threads.
Having a match stopped part way through a game is fairly rare and if it does happen, it is almost exclusively in the lower leagues (except when an asian betting syndicate has their finger on the off switch for your flood lights)
I think matches being postponed due to weather should come back, again, especially in the lower leagues. THis is a frequent occurance in the winter months down there. Not so much for the top teams and their fancy pants undersoil heating etc. though.