Can you increase the size of an image without losing quality?

Any time I get repeat questions, I like to share the answers here because I assume that even more people would like an answer!

​Most recently, I've gotten this question several times:

Q: Can I increase the size and resolution of a digital photo?

A: Unfortunately, you cannot enlarge an image - it will only highlight the poor quality of the low pixel count. The only options are to find the original large version (the photographer should have it backed up in multiple places) or use an alternate image.