In most cases, clearing the preferences in InDesign takes care of these hiccups. You can easily trash the preferences by holding down CTRL+ALT+SHIFT while launching the program. Just make sure you save your custom settings before you do that, otherwise, you'll loose everything. In version CC and forward, simply sync your custom settings in preferences (CTRL+K), under "sync settings" section.
I am a student working for my college's IT department as an assistant. After some troubleshooting on a student's machine that was experiencing problems with Indesign crashing upon opening, I found that removing the "font.lst" files worked to fix the problem.
I am not sure if this student has recently installed a new font incorrectly or is using a corrupted font, so I don't know what the possible cause of the problem may be.