The first thing I printed, was a Calibration clube. After printing a few upgrades, I went ahead and printed a temperature tower. This one seems to work well, and you can only get the gcode in the files section. It has the temperature changes built into the gcode. Print this for each new roll of filament, to find out what temperatures are optimal. Finally, we have the Benchy. The benchy is used far and wide to show off what the printer can do. Probably more so than the calibration cube. Finally, here is a very simple test that uses very little material.
Bed Leveling Calibration
Next up, is bed leveling. You can find a number of models to do this on Thingiverse, but this one seems pretty simple and has an ample selection of places that it prints to see how level your bed is.
Calibration Torture Tests
Next up, is the torture tests. They come in the guise of calibration, but they really are meant for one thing… push your printer to its limits and beyond, and let you see how well your printer can perform. There are a great number of these, including this one and this one that is listed as a torture test. This is a good way to see what your printer is capable of.
Just for fun – old school calibration
If you want to go old school, don’t forget about the venerable Yoda Bust calibration example. Finally, if you are feeling kind of ambitious… you can go old school with purpose. The infamous Yoda Bust – Soap holder!
I hope this helps give you some guidance of where to find some different items for calibrating your printer. I’d say at the very least, print the Cube regularly, especially after major upgrades, and the temperature tower with each new roll of filament. This will give you a good base line functionality on your printer. The bed leveling model is useful, but many people print a wide brim and get a feel for what the first layer should look like and use that tweak in their printers.