[codebaobab]

Right. And just to drive the nail in a bit deeper: ending a sentence with a preposition is a grammatical construction that English gets from its roots as a Germanic language. German has what are called "separable verbs" where prepositions are combined with verb roots to create a new verb. In certain cases, the preposition prefix is split off of the verb and placed at the end of the sentence. The preposition must come at the end of the sentence in order to be grammatical. You can see remnants of separable verbs in English:

"I passed the man in the red hat by." pass-by

"I threw all of my old, useless papers out." throw-out

To repeat the parent's point: the stricture against ending a sentence with a preposition is simply a bias for grammatical structures that English inherited from Latin (through French) and against structures inherited from German.

The rule against splitting infinitives falls into the same category. It is not possible to split an infinitive in Latin because infinitives aren't made up to two words.

Again, these two rules (and others like them) are about biases, not about grammatical correctness or even clarity of communication. When you say "Who am I speaking with?" and "To boldly go where no man has gone before.", no one is actually left scratching their heads and thinking "I wonder what he means?"

[colanderman]

I would never say either of those sentences.

"I passed by the man in the red hat."

"I threw out all of my old, useless papers."

Both of those not only keep the preposition away from the end of the sentence and keep it near the verb to which it belongs, but most importantly they sound more natural.

Your example of "Who am I speaking with?" follows this same pattern -- "with" is kept next to the verb "speaking".