Sure -- there are lots of them! You can get free Gems by playing My Little Pony to collect daily rewards; playing the (awesome) Balloon Pop game; leveling up; collecting them in the Crystal Mine; finishing Quests; finding Derpy, the pony in the box; completing Pony Collections; playing the Equestria Girls mini-game and reaching reward thresholds; defeating Parasprites; taking part in some special Events; watching videos in the "Gems" tab of the in-app purchases section; receiving occasional offers to get Gems for watching a video with advertising; collecting them from Gem Shops, such as the Houseplant Shop; and inviting new friends to the game (when invited friends reach certain VIP level, you can claim Gems in the Friends tab of the Profile menu).