Each of the Source Code repositories come with a free tier but each has their own restrictions

BitBucket from Atlassian is free for small team up to 5 users or you can self-host for up to 10 members for one time fee of 10$. With the free plan in cloud, you can have unlimited public and private repositories.

GitHub doesn’t allow private repositories at this time. While you may host closed source project there, I wouldn’t recommend it.

ProjectLocker provider a free tier: 1 user, 1 project and up to 50 MB of storage.

All three supports Git which is probably the most widely used Source Control system these days.

Of the three BitBucket stands out in hosting closed source private repositories for free. Overall their pricing is most lucrative in the long run.
GitHub, while not free, has the most traction.