Why is the expression "Speak of the devil" and not "Speaking of the devil"? For me, the -ing would make more sense because you're currently talking about someone, when he/she appears.
For example, if you're talking about something, and that subject made you remember something else, you would say something like:
Speaking of groceries, I have to go to the supermarket in an hour.
but you wouldn't say:
Speak of groceries, I have to go to the supermarket in an hour.
"Speak of the devil" is the short form of the idiom "Speak of the devil and he doth appear".
The proper use of the phrase "speak of the devil" is not in the context of remembering something or one thing reminding you of something else. That kind of context is where you might say "speaking of groceries" as in your example.
The proper use of "speak of the devil" is when you are speaking about someone - usually having something bad to say or some kind of gossip when that person suddenly comes into earshot. This is appropriate insofar as "speak of the devil" is short for "speak of the devil and he will appear" as was pointed out by Jeff.
It can also be used ironically in a situation where a person joins you in mid conversation, even if this person was not the subject of the conversation. It is an often good-natured jibe on the premise that you may have been gossiping about the person or that you are comparing them to the devil.
In this case, "Speak of the devil..." is a partial quotation of the idiom "Speak of the devil and he shall appear." (or one of its several variants).
"[Do something] and [something will happen]" is an elliptical construction that means "If you/one [do(es) something], [something will happen]".
Note that "do something" is an infinitive in the "[Do something] and [something will happen]". "something wil happen" is usually a present-tense or imperative verb form.
For example:
A similar construction replaces "and" with "or" to mean "if you don't do something, something will happen":
Note that "Speaking of groceries, I have to go to the supermarket in an hour." is a completely different construction.
The full form of the phrase is an example of the construction described above:
So in essence, the idiom means that speaking of e.g. someone absent or some undesired situation is tempting fate, because that person or situation may appear.
Language meaning changes over time so quoting 100 years back or more is not all that useful although you could win on Jeopardy.
"Speak of the Devil" by its usage today simply means someone stepped into the room who you were talking about. It's used so casually now that it has no real meaning other than that.
It's similar to people saying "How yah doing" as there is no point of putting a question mark after it. That literally means "hi" now and you don't expect someone to actually answer.
As a side note...trying to logically figure out why the phrase doesn't include "ing" is also hinting that the English language somehow has rules anymore. It's a hodgepodge of languages at this point. Only a small fraction of society actually remembers the rules and those are usually copy writers and patent lawyers. It also depends on where you are in the world as grammar is so subjective.
