My left hand crank split. Luckily I had a spare, but getting the pedals off of a bicycle can be a problem. A normal shifter sometimes has jaws that are too wide to fit the gap between the pedal cage and the crank. That is when you need a pedal spanner.
View of a typical pedal spanner
A pedal spanner (an example shown above) has the narrow spanner end which fits into the gap between the pedal cage and the crank, and is also reinforced to take tight pedals off. The trick I found was to sit on the seat and put my foot on the other pedal, and then fit the spanner into the pedal that needs to be removed.
Using my foot on the spanner I pushed it towards the back of the bike and presto, the pedal came loose. Unfortunately sitting in this position made it hard to photograph.
Side view of a typical pedal spanner
Beware when removing pedals, that the threads are opposing, so one pedal will turn anti clockwise to be undone, and the other side will turn clockwise.
The other end of the pedal spanner has a socket which fits the end nut on some pedals, so that you can take them apart to service them. If you are in the habit of taking pedals off quite often I highly recommending getting one of these spanners specially designed for the job.
Another example of a pedal spanner:
Here is a different spanner
