I just found for myself mecabricks.com. Amazing! However I wonder where do they take models of their parts from? Are they all self-designed (and proprietary) or come from some open source? Is there any open library of parts ready to be imported into a 3d editor?
LDView is probably the easiest way to export parts, and it directly supports exporting POV, 3DS, and STL formats. By default the parts exported will not have smooth curves on subparts, such as studs. This may be important depending on how realistic you want you model to look in your 3D software. This can be changed in LDView by clicking on the Edit > Preferences... menu item, then clicking Primitives tab. From here, uncheck the Low Quality Studs checkbox. You may need to close and then open LDraw again to see the change.
Further update - as pointed out in the comments, I had incorrectly stated LDraw was the program that I use to export shapes to STL format. That program is actually LDView, and makes use of the LDraw library. I've updated the link to include the correct application. Apologies for the confusion.
Also, while I'm editing this, be aware that some of the shapes exported to STL format will need adjusting. Bushings and axles come to mind, as these parts will not fit together unless the axles are sized slightly smaller. Technic pins will also have similar issues due to the end flanges not being slightly chamfered as the are in real life. You'll need to make adjustments if you want some technic parts work together. Some parts also don't always correctly reflect that they have an "inside", so some areas of parts may print as hollow voids rather than with the desired infill. Check for this using your slicer software before printing.
Most, but not all, existing LEGO oriented 3D modelling systems make use of the open source LDRAW libraries. Downloads, specifications, and more information can be found at https://ldraw.org/
There used to be PrintABrick, but the website has been down for ages. You can still find the code on github if you want to run it locally: https://github.com/hubnedav/PrintABrick