Is there a solution for OS X 10.6? I don't find it in the system preferences.
You can try using Ukelele to create your own keyboard layout, without the dead key behaviour.
The three characters you mention '~', '^', and '`' are all on my (UK Apple) keyboard - '~' and '`' are on the key to the immediate right of the left shift key (I believe this is above the tab key on US Apple keyboards) and '^' is shift-6. Try turning on the "Keyboard & Character Viewer" in the input sources tab of the language and text section of System Preferences. Then select "Show Keyboard Viewer" from the menulet that appears in the top right of the screen - press the modifier keys and you'll be able to see what buttons do what.
Nontheless, to get other diacritical marks and whatnot on their own, you can press a key that can't have that accent on it. For instance, to produce '\´', you can press option-e and then escape or any letter key that can't take the accent (for instance, w).