There are some good answers here already, but some of the comments betray an unfamiliarity with the social system that Tolkien was portraying in the Shire.

The Shire is very specifically based on the rural English Midlands of the late 19th century that existed, although already starting to disappear, when Tolkien was growing up. In that society, there was a very clear distinction between the different classes. Frodo represents the landed gentry - not actually aristocracy, but powerful and influential as a result of owning large amounts of land. It's not made explicit, but as owner of Bag End he was almost certainly also the owner of much of the land about. The Gamgees may well have been his tenants.

Meanwhile, Sam is very much of the servant class. If you've seen the TV series Downton Abbey, for example, you can picture the sort of character he's meant to represent. Being "in service" was regarded at that time as a very good occupation for someone like Sam. He became very close to Frodo, and devoted to him, but the relationship was never one of equals. Sam would never have dreamed of referring to Frodo without the honorific.

Even Faramir, from a completely different society, recognizes this relationship, and tells Sam:

"Patience!" said Faramir, but without anger. "Do not speak before your master, whose wit is greater than yours." The Lord of the Rings - Book IV: Chapter V - The Window of the West

After Frodo sails from Middle-Earth at the end of the book, he leaves Bag End to Sam. At that point, Sam is himself propelled into the gentry: he becomes Mayor, and founds a dynasty of his own.