Please note: this is not the right answer, although I hope it continues to be useful. NB it has been made a "Community" answer so I don't receive any points from upvotes
To see all commits for a specific branch (so this does NOT actually answer the original question, which is to see commits across all branches):
Click "Code" (left-most tab) on the main page for the repository. Under those 4 buttons ("master", "Go to file", "Add file", "Code") there is a blue rectangle. At the right end of that is a clock icon and a number. If the viewport of your browser is wide enough it even includes (hurrah) the word "commits". This is a link. Click and ENJOY!!!
NB the URL for this page is like this: https://github.com/myProfile/myRepo/commits/master

Please note: this is not the right answer, although I hope it continues to be useful. NB it has been made a "Community" answer so I don't receive any points from upvotes
To see all commits for a specific branch (so this does NOT actually answer the original question, which is to see commits across all branches):
Click "Code" (left-most tab) on the main page for the repository. Under those 4 buttons ("master", "Go to file", "Add file", "Code") there is a blue rectangle. At the right end of that is a clock icon and a number. If the viewport of your browser is wide enough it even includes (hurrah) the word "commits". This is a link. Click and ENJOY!!!
NB the URL for this page is like this: https://github.com/myProfile/myRepo/commits/master

This is an old feature of GitHub but not really that intuitive.
Using the GitHub website:
- Click a project
- Click the 'Insights' tab (moved inside the Meatballs menu)
- Click 'Network'
- Click on the 'node/circle' for each commit to go to that commit.
Diagram below.

Additionally, you can drag to the left to see all commits throughout time for all forks and branches.
Github commit history
View commit history of individual files
What is the best way to view a repo's git history quickly?
Is there a way to show all the commits history in a single page, since the very first commit?
Videos
In github why I cannot see the all commits history I have made in a single repository? I cannot see the option to see all my commits history. It would be great if I get help on this . Thank you!