If I farm, I'm a farmer. But if I guard, I'm a guard?

One who farms is called a farmer.

One who waits is called a waiter.

One who dives is called a diver.

One who programs is called a programmer.

But one who guards is called a guard.

How did it come to be that this word dropped its -er ending for its noun, and are there other examples like it, sharing any commonalities?

Dictionary.com lists guarder as a noun, implying that it can be used instead of guard (and has an example sentence). But from my experience as a native American-English speaker, I can't recall it ever being used outside of poetic-style writing. Both dictionary.com and merriam-webster list guard as coming from the Old-French guarder, but I'm not sure why this word was special and dropped the -er.

You can't drop what you never had. Guard (noun) according to the Oxford English Dictionary comes from:

French garde, earlier also guarde (= Italian guarda, Spanish guarda) < Romance *guarda, < Old Germanic *wardâ.

The noun "guard" predates the verb in English. The verb to guard comes either from the noun or from the same French word the noun comes from. For some reason, as you note, there is a word guarder (formed from guard (verb) + er) that came into being after both the noun and verb forms of guard (which looks like it was a lot more popular some hundreds of years ago, but isn't really used now).

Interestingly enough some of your examples aren't really examples. Farmer, for example, wasn't originally formed from the English words farm + er. The OED lists its etymology as:

Anglo-Norman fermer (Britton), French fermier < medieval Latin firmārius, < firma : see farm n.2 Now usually apprehended as agent-noun < farm v.2 + -er suffix1; some modern uses may be properly regarded as belonging to this formation and not to the older word.

_{In the early recorded forms the suffix -er has been replaced by -our, so that the word apparently corresponds to the synonymous medieval Latin firmātor, one who takes something on lease (Du Cange), agent-noun < firmāre in sense to contract for, become responsible for.}

Similarly, waiter wasn't formed in English originally according to the OED:

Originally < Anglo-Norman *waitour, Old French weitteor, gaiteor, agent-noun < weitier, gaitier wait v.1 In later use < wait v.1 + -er suffix1.

How about these, examples of professions that are both verb and noun where the verb expresses the work that the person typically does:

• guard
• coach
• cook
• guide
• host
• judge
• nurse
• pimp
• scout
• smith
• spy
• whore

As to the etymology of guard, Etymonline says the follwing:

from Middle French garde "guardian, warden, keeper; watching, keeping, custody," from Old French garder "to keep, maintain, preserve, protect"

So I presume garde first had an abstract meaning, more like "the phaenomenon of guarding", and as in "be on your guard! en garde!" or "my guard" denoting the body of men that guard me; and then it also came to be used for a person doing guarding later.

It appears that English only dropped the -e from the French profession after borrowing the noun. Since -e is unstressed and often mute or even silent in French, it isn't very surprising that it should have fallen off. In fact, there are countless nouns in older English that dropped an -e. Cf. the (probably anistorical) trope ye olde [noun].