At the school I'm a governor at we have link governors for each subject and also for each year group (2 form entry) - they stay with that year group (so if they have YR this year they have Y1 next year, etc.) Works very well.
I'm a school governor and we are each link governors for a particular class and a subject. It's great being a governor to a class. We get to go in regularly to spend time with the class( if we want), go on any trips/to class assemblies etc
I should have added that as subject link governors we are expected to observe the subject being taught across the school three times a year and we fill in a form which is submitted to the Chair of Govs and shared at meetings. Used to be OK as we were infants only, but we're now a primary so they may rethink this slightly.
The reason this was introduced was in response to an Ofsted suggestion a few years ago, to facilitate govs knowledge of subjects/levels/issues for teachers etc.
We have governors linked to key strategies the school is implementing. We've just moved to this system and away from being linked to subjects. I think it focuses us more clearly on the school's strategic development.