I made my first game in unity, and I was wondering if I can sell it without owing anything to unity?
From the Unity FAQ:
Are there royalties or a per-title fee?
No, Unity does not charge on a per title basis and you do not pay royalties or pay revenue share, even for games and applications made with the free version.
Can we sell games and make money with the free version of Unity?
Yes you can create and sell a game with the free version of Unity, without paying royalties or any revenue share. However, the free version of Unity may not be licensed by a commercial entity with annual gross revenues (based on fiscal year) in excess of US$100,000, or by an educational, non-profit or government entity with an annual budget of over US$100,000.
Please also be aware that the feature set of the free version is not intended for the production of professional games and interactive content. Lastly, games made with our Pro trial licenses may not be distributed nor used for commercial purposes.
This is also mentioned in the Unity Software License Agreement. Note that Software refers to the Unity software. The game or application you are creating is the Licensee Content (See section 13. Definitions). The section quoted in the other answer tells you that you can't distribute the trial or educational versions of their software runtime. With other versions, you may distribute the software bundled with the game you created.
No, they don't own your game.
But they do own their engine. In Unity's EULA you can find relevant information about how the license between the developer and Unity works out.
- Grant of License
Use Rights. Conditioned upon your compliance with the terms and conditions of this Agreement and payment of all applicable fees, Unity grants you a non-exclusive, non-transferable license: (i) to install and execute the executable form of the Software, solely for internal use by a single person to develop Licensee Content; and (ii) if you have licensed a version of the Software other than a trial or educational version, to distribute the runtime portion of the Software, on a royalty-free basis, solely as embedded or incorporated into Licensee Content and solely to third parties to whom you license or sell Licensee Content pursuant to an agreement that is no less protective of Unity and its licensors as this Agreement. You may not sublicense the rights granted under clause (a)(i), but you may sublicense the rights granted under (a)(ii) solely to third parties to whom you license or sell Licensee Content to act as distributors thereof pursuant to an agreement no less protective of Unity and its licensors as this Agreement.