How to set the default branch in GitHub.com?

Do you have to be the repo owner?

Yes you do.

How to set the default branch on github.com when I go to browse commits.

If you fork the repository, you can change the default branch of your fork, by clicking on the Settings button (see below).

This will allow you to pick your favorite branch as the default one for your own fork, but you'll have to keep your forked repository in sync with the upstream repository by yourself.

Or you can directly jump to the following url https://github.com/{:user}/{:repo}/settings

Just log into your GitHub account and on the far right side in the navigation menu choose Settings, in the Settings Tab choose Default Branch and return back to main page of your repository.

Here's a visual for the answer:

2021 Update

The current GitHub UI has changed quite a bit -- what used to be buttons are now tabs across the top of the repo's home page:

Click the Settings tab then, on the left, click Branches:

Mousing over the switch branch icon (right/left arrow, bottom right of pic) pops up a hint. [or click the pencil icon to give the default branch a new name]:

Clicking on switch branch pops up a list of branches:

Select the new default branch (I chose master), click Update, and acknowledge that you know what you're doing:

Voila!