The C64's primary competition in the US in the '80s were the Atari 800 and Apple II, and it was highly superior to both in terms of graphics, sound, memory, price, and pretty much everything else. In Europe, and especially England, it competed against the Sinclair ZX Spectrum (which was a joke of a computer that somehow managed to be a success) and the Amstrad CPC (which was almost on par with the C64 and somehow managed to be a failure). It had several impressive features for its time: hardware-accelerated scrolling, eight hardware-accelerated sprites with automatic collision detection, and rudimentary scaling. It could also mix high-resolution and high-color graphics modes, providing extra detail in games; no other computer of the time could do this. Its software library is miles ahead of any other 8-bit computer, with thousands of games (some of its shoot-em-ups are good enough to rival R-Type), several word processing and spreadsheet applications, a few graphic editing programs, and even a window-based GUI. The C64 demoscene is still strong today, producing demos, graphics, and music that would have been thought impossible back in 1982 when the C64 was first released. The C64 is a true classic, and it deserves all of the respect that it gets.
Because the Commodore's keeping up with you!
--Commodore 64 jingle/slogan