You can't actually delete a goal. All you can do is make it 'inactive'. However, this isn't very satisfactory since you can only set 20 goals within a profile (4 sets of 5). Justin Crutoni, Google's Analytics Advocate give this advice in his book 'Performance Marketing':

Set up two additional profiles, 'Raw' and 'Test':

-- Raw, this is a backup so you never add filters or goals to this profile;

-- Test, use this profile to experiment and test new things including goals.

Adding these two profiles reduces the need to delete a goal because you've tested it and seen the results. Once you're happy with them, you can create the goal in your main profile.