If you want to play Space Invaders or Space Invaders Part II on your PC, you will obviously need to get yourself an emulator that is capable of running these games.
The main emulator I use and recommend is the Multiple Arcade Machine Emulator (MAME). This emulator is available free as a download from many sites. It is capable of emulating a very large number of original coin-op arcade games and the current version, 0.30, can now emulate Space Invaders and both the Midway and Taito versions of Space Invaders Part II. All the screenshots on this site were taken using MAME.
If you would like to get hold of the latest version of MAME you can get it from:
The Official MAME Emulator Page
If you would like to play the original version of Space Invaders but on a Super Nintendo Emulator (strange I know, but there is no accounting for personal taste) you will need to get hold of a SNES emulator and an image of the cartridge ROM. The ROM is currently available on the Downloads page of this site. The SNES version supports simulated screen backdrops that were used in the various cabinet and table-top versions of the game and is a perfect emulation of the original game, with all the features mentioned on this site intact.
Engine Trouble in Taito's version of Space Invaders Part II (Shoot the flashing ship to see this)