Hagrid is virtually the only occupant of a 'middle ground' in the Hogwarts hierarchy.
The two principal 'classes' (for want of a better word) at Hogwarts are the pupils and the staff. Within the classes everyone calls each other by their first names - Harry calls Ron 'Ron', and Dumbledore calls Snape 'Severus'. But pupils call staff by their last names, and staff call pupils by their last names (excepting those that are exceptionally close, like Harry and Dumbledore).
Hagrid is lower than staff, but higher than pupils. It's entirely applicable for pupils to call him Hagrid (since he is above them) and same for staff (since he is below them).
Note that Filch is in the same position, and is universally referred to as Filch, not Argus.
You could argue that Harry, Ron and Hermione become close friends with Hagrid, and they could probably get away with calling him by his first name. Probably they don't because old habits die hard, because everyone else calls him Hagrid, and because it's easier to start calling those below you by their first names - Dumbledore calls Harry 'Harry', but Harry never reciprocates.
Some of this is indeed related to the British tradition of school stories, where teachers and pupils both call each other by their last names.
EDIT: Doing a little rethinking here, I believe that while what I've written above is correct, it is only a partial explanation. When pupils address staff, they don't call them just by their name, but with an honorific - "Professor Dumbledore", for example. (though they may just call him 'Dumbledore' when he's not there) If this were the only factor, Hagrid would properly be addressed as "Mr. Hagrid", just as Filch is properly addressed as "Mr Filch." This doesn't happen. So @Valorum 's explanation is at least as significant as mine - Hagrid is addressed as Hagrid because that's what he calls himself.