I'm already at the limit of 9 and most of them are 5km eggs. Is there any way to get rid of them? I want to make space for 10km eggs because I hope they contain rarer Pokémon.
The ability to delete Eggs has still not been introduced to the app, however this is certainly a feature that Niantic will be forced to implement in the near future.
If you want this feature and hope to contribute to the cause, click on the 'Pokéball' while in-game, followed by the 'Settings' button to 'Report High-Priority Issue'.