The most common class of useful objects to print that you can find on Thingiverse are upgrades and accessories for 3D printers. Once you have a 3D printer working, you can improve upon it by printing more or better parts.
Dislike having to manually unroll plastic filament and leave it laying on the floor for your printer? Add a few inline skate bearings to this Spool Roller STL file and you’ve got a snap on auto-rolling filament spool mount for your printer.
Having issues with wires going everywhere? Print a few snap on wire clips that will hold them to your frame rods…
Is your Z-Axis end-stop too difficult to adjust? Print the parts to build an upgraded model (with $5 worth of parts from the hardware store) with a bit textured knob for easy adjustment.
Think your current printer is getting old? Have it print parts for the next generation printer….