I've read many pages that point out that many office applications allow for this by typing the code followed by Alt + X, but frequently, I want to insert a symbol when I'm not in one of those applications. Is there a universal way to achieve this?
The character map is useless, unless you have time to manually search through all the characters available.
I posted the question at Super User, and basically, the response I got there was to use Alt codes for the symbols. However, I discovered that, on the whole, these only work for the first 256 Alt codes. So basically, the answer to my question is "No, there's not a good way."