I'm going to go with the premise that they do not wear out. I've long downloaded and stitched together videos of solar activity captured by SOHO, or the Solar Heliospheric Observatory satellite. That satellite was launched in 1995, went operational in 1996, and is still sending back images. Its CCDs get POUNDED by solar particles, high energy protons and other radical forces on a continual basis. Dozens of times a year it takes direct hits from CME's (Coronal Mass Ejections) and other explosive flare events.

There are periodic "CCD Bakeouts", where the sensor is heated for a period of time which reduces temporal effects of the particle storms it endures. After a decade and a half, the images from SOHO look as good as ever. And while, granted, this kind of sensor is scientific grade, it also takes a beating a thousand times worse than any camera sensor will (or probably could)...CCD or CMOS.

So yup, I'm gonna go with sensors don't wear out (not in the normal lifetime of a camera.)

Regarding shutters, they do have a specified lifetime, usually in the detailed specs. They can last anywhere from 15,000 actuations to several hundred thousand actuations, and sometimes its the luck of the draw. If they do wear out, they can be replaced, for a fee, but often a fee far cheaper than a replacement camera.