Other distinctive breed-specific personality features of the Maine Coon:
Fondness for water
It is widely believed by cat experts that Maine Coons are a natural breed derived from selection in a sea-faring environment. Cats were frequently kept about trading vessels as pest control, and may have done some disembarking into fairly harsh climates, breeding, and returning shipboard. The thinking is that this eventually resulted in a domesticated but hardy breed of cat largely unafraid of water and possessed of a fine, silky coat of water resistant fur, the result of breeding between European longhairs and domestic North American shorthairs. The Maine Coon's unusual response to water is another distinctive feature of the breed.
My Maine Coon (Zoë) does not have any interest in swimming, but loves to play in water. She bats at the stream of water coming out of the sink tap, and will happily sit on the very edge of my bath and periodically dip her paws in, shake the water out, repeat. She also likes to splash in her water bowl. I have read that this business of playing in the water bowl is "scraping the leaves/scum/etc. off of the water's surface" behavior. She enjoys spending time in the bathtub and in the sink when they are dry.
The Maine Coon's Voice
Most Maine Coons speak in emotive trills and chirps rather than the usual vocabulary of meows, unless the cat feels the need to be emphatic, in which case he or she may loudly state "ME!"
Many Maine Coons will happily play fetch with their human, retrieving small objects (like small wads of crumpled paper) and carrying favorite toys around in their mouths. They can comfortably sit on their hindquarters and hold something between their paws, although I have personally seen this very rarely. However, Zoë does like to sit "human-style" on one of my chairs, sitting on her rump with her back legs out in front of her and her back to the back of the chair, front legs curled to her chest, dozing.
Getting Along With Other Animals
I was somewhat surprised, but not entirely so, to find out that getting along well with other kinds of animals is actually a common breed feature in the Maine Coon. Zoë is extraordinarily friendly with other cats (often to their dismay), and is very fond of my parents' Golden Retriever, with whom she plays and naps when we go for visits.
Maine Coons like to be where their owners are, and will follow them nonchalantly from one room to another. This includes the bathroom. Many Maine Coons are not lap cats, but want to be in the tableau anyway. Having an extra chair or a place in your working area where the Maine Coon can curl up and keep an eye on you would be appreciated. Zoë, at the relatively advanced age of six, spontaneously developed a fondness for lying across my shoulders like a fur stole while I work. She curls her tail around my throat, drapes her legs off my left shoulder, and rests her head on her paws on my right. She watches me type, and periodically butts my chin when she wants some attention.