Mr. Game & Watch was just a placeholder figure to represent various characters in the old Game & Watch handheld titles, such as a Diver, a Fireman, and even Mario. He was most likely included in Melee as a tribute to Gunpei Yokoi, the creator of the Game & Watch, Game Boy, & Virtual Boy as well as Shigeru Miyamoto's mentor.
Sakurai said on the Japanese Melee site that the Ice Climbers were included solely as an NES era representative. Others that were considered were Excite Biker, Balloon Figher, and Pit. Excite Biker wasn't included because he'd have to stay on his bike at all times, Balloon Fighter wasn't included for not having many possible moves, and Pit wasn't included because, until Brawl, they couldn't think of a way to use his bow for close combat.
I'm not sure why R.O.B. was included in Brawl. I've never heard of him being extremely popular anywhere, even if he's well known and loved in most places to an extent. It may have been that Sakurai wanted a surprise character.
I noticed you posted about your hated SSBB characters. Something you said made me kinda... Intrigued. Game and Watch not being a real character? What do you mean by that?
As for Ice Climbers, maybe they are more popular in Japan than you think ( I don't really know...). R.O.B. was added as he was wanted due to popular demand in Japan, I think.