Although I believe there are widely said to be seven distinct generations (single-game consoles/TV overlay consoles/consoles without microprocessors, Atari 2600, NES, SNES/Genesis, N64/PS/Saturn, Dreamcast/Xbox/PS2/GameCube, 360/PS3/Wii), you could broadly say there are three large generations.
The first was games largely without "levels" or "game worlds" and featured a single game mechanic. Sound was sporadic and crude and graphics were the most primitive that allowed gameplay objects to be distinguished, with enormous pixels and minimal (if any) coloring.
The second was the "2D" era. These games featured detailed, representational, full-color graphics, large game worlds, and fully composed background music.
The third and current is the "3D" era. These games also include vast amounts of multimedia, such as fully-voiced games and in-game video.
Innovations in controllers happened at each generation, so I don't think control defines them. Similarly, online play, although only having really exploded this generation, was seen as far back as the SNES and Genesis (yes, there were little-known accessories and services that actually worked on those systems), so I don't think it's defining.
Obviously, there are huge differences between the earliest and latest games within each of the broadest generations.