Why doesn't Cmd + Space work?

To set your hotkey, go to the Alfred preferences and view the General tab. Type your key combo (ctrl, alt or cmd + space/character) to set it.

Check it isn't in use by Spotlight

If cmd + space doesn't work, that hotkey may be assigned to another feature. First, verify that it's not in use for Spotlight by opening Spotlight's System Preferences and disabling the menu keyboard shortcut at the bottom of the preferences pane.

Check it isn't used for language switching

If you use multiple languages on your keyboard, it's likely to be used for language switching.

Here's the procedure you will need to go through:

  1. Open System Preferences
  2. Go to Language and Text
  3. Tick a second language if you only have one set (the System needs at least two languages to toggle between in order to allow the keyboard shortcut to be changed)
  4. Go to Keyboard > Keyboard Shortcuts > Keyboard & Text Input (On Snow Leopard, this falls under Universal Access)
  5. Untick "Select the previous input source"or set it to an alternative key combo

Even if you are not actively using that key combo for Spotlight or language management, OS X may be reserving it behind the scenes. If that is the case, in the Input sources, select a second language then go to the Keyboard & Text Input section again, untick the two checkboxes relating to input source.

You can then go unselect that second language, once the key combos are changed or disabled.