This question is up for debate.
Some say Missingno does nothing. Some say it does nothing as long as you do certain things or take certain precautions. Most people, like PokemonBlack10 above, say it will freeze the game, corrupt your save data, and force you to restart your game.
My question is why did you say, "on my computer"?
If you mean that you are playing the game as a ROM on your real life computer, than capturing Missingno will not damage your real life computer--its data is part of the game and the game's data, not your actual computer's data. The only way the ROM is related to your real-life computer is that its files and the emulator files are on your computer.