Is hacking a computer game illegal

Yes, it definitely is, though it depends on what you mean by hacking. Maybe you mean downloading a costly game for free by getting it cracked or decoding the game in your PC for some changes. To do anything like that, you'd need the permission of the game's author. Without such permission, it's illegal. Hacking ANYTHING is illegal!

Now, if you mean modifying a game that you own for you own purposes, and you are not going to distribute it in any way, or all you distribute is the means to alter the game, then there is nothing wrong with that. Sometimes you can patch bugs or change the graphics or other resources. There is no intent in that case to defraud anyone. However, the license or terms of use for the game may tell you not to do this and that your rights to use the game are null and void if you do so. But nobody will know that you modified your own legally-purchased copy. Whether such a "shrink wrap license" has any legal weight against you making mods to games you own, that depends on your jurisdiction.