Can I get pokégold without paying real money?

Solution 1:

You may get bonus gold from the Defender Bonus every 21 hours. To claim your bonus, tap the little shield on your Shop screen.

In order to be eligible for this, you must have Pokemon stationed on Gyms. Each Pokemon confers 10 Pokecoins / day, up to a limit of 100 / day.

Solution 2:

You can get some coins without paying real money with your defenders bonus. You can get a daily bonus each day dependent on how many gyms you have a Pokemon on. During the beta, it was limited to 10 gyms for reward, but I've only had one day to test. I received 10 coins for having one gym this morning.

You can get this bonus by opening the shop and clicking on the shield in the top right corner.