Strange Characters Abound

I've been having very strange issues, mostly manifesting through my web browsers (Chrome & Safari, mostly), though occasionally through my OS (currently running Mavericks 10.9.1).

What's happening is that whole text areas are being replaced by strange, odd characters that make the pages impossible to read. See this for an example: ).

This issue actually started when I was running Snow Leopard (10.8.6 was my last version). It’s showing up primarily via Chrome or Safari, very frequently via Yahoo pages and links, email, etc., but I've also seen it occasionally pop up and replace the date on my Calendar app on the dock (!?!).

If anyone has had the same issues and knows of remedies, please let me know. It’s very annoying and frustrating.

Thanks

I have seen that before -- what happens is that a vital system font is moved or tampered with, or the system Fonts folder generally messed with. Can also be caused by running Monolingual (or "cleaning" programs like that) too aggressively. Lastly, its possible that something damaged the fonts the system is looking for that is not directly the users' fault (for example, on occasion I used to see that Microsoft Office installs would dutifully replace the system Times New Roman with its own, but that was a long time ago).

Have you tried changing the default fonts on your browsers to different ones, and if so did that make any difference?

Thanks, Chas, for the in-depth answer. It very well could be that one of the system fonts was moved inadvertently on my part. I have both FontBook and another font app manager that are possibly in conflict and I need to sort that mess out. I will look into it once I get a chance. Will update when I get the chance. Thanks, again...