I think Han breathes life into the OT... without such a character, it would be a distressingly earnest, po-faced affair... his character is there to subvert that aspect of such a grandiose, operatic story... I have to say, in my later years, the dialogue between Han and Luke about Leia as they travel to Yavin has delighted me more and more... I didn't really 'get' that when I was younger... I mean I understood it... superficially... but Ford really loads that short scene with playfulness and good humour...
The dialogue between him and Leia in ESB is so good... again, it brings humour and humanity into the film... "my hands are dirty too... what're y'afraid of...?"