I think all the noclip answers are wrong, noclip doesn't work like 'noclip 1' and 'no clip'
Actually, you have to open up the console, either by pressing the tilde key or launching Portal with the launch option '-console' (set this in Steam), then when you are in game , type sv_cheats 1 and afterwards simply noclip
Also, it is probably not in all of the maps, so you might have to try this in different parts of the game. Your best bet is trying this right before the GLaDOS boss fight.