Good point.
Pronouns. A demonstrative and a personal, respectively.
English is not my first language, so pardon me if it isn’t to the Straight Dope standard up. 
Perhaps not, but a similar construction is gaining prominence: “come with.” For example, “I’m [We’re] going to the park. Would you like to come with?” I am not sure if “with” is replacing “along” or if there is an unstated object (“me” or “us”) at the end.
Anyways, the only proscription I am aware of is that you should not use unnecessary prepostions to anticipate the answers to questions. Hence “Where’s the food at?” is non-standard English. In my mind, it is regarded in the same way as “ain’t”–non-standard to the point of derision.
I think this is a good example of why not to end a sentence with a preposition.
When you say “I need something to eat my crab …” it sounds like “something” is eating the crab. Then when you say “…with” it is clear that the speaker will be doing the eating.
When the whole meaning changes mid sentence, it can feel a bit jarring.
“I need something with which to eat my crab.” flows better, if a bit fancy sounding.
“Come with” is a Midwestern construction (possibly even as narrow as Illinois/Wisconsin/Minnesota), so far as I know. I grew up with the phrase being perfectly normal in my (Chicago) dialect, but I found out with greater exposure that it’s considered non-standard elsewhere in the US for the most part. I want to say that it comes via the German influence and the verb mitkommen, but I’m not absolutely sure.
I asked this before but I don’t see anyone addressing it directly. So, I’ll ask again, “is it a worthwhile rule to follow with exceptions?”
I find that it can keep things concise and clear in many cases. But, I’ll admit that other times it makes things unnecessarily wordy. Still, overall, I think it helps.
What say you?
I think that you should try to be a little more ambivalent. These stark black and white opinions don’t help.
Seriously though, it’s a silly rule with silly origins and provides little value to one’s ability to write well. And I’m still not sure you’re at all clear on what a preposition is, or what it means to have one in the terminal position of a clause.
Well, I’m trying to be a bit more ambivalent by allowing for exceptions.
I agree. I don’t think I understand it fully either.
No, it’s not.
Inverted word order in English is expected in questions: E.g. “Where are you going to?” v. “To where are you going?”. It’s also expected when creating emphasis: “Hell! That’s where I’m going to!”
Outside of questions and inversions for emphasis, prepositions don’t get dangled much. In order to dangle a preposition, you’d have to go out of your way to do it, which means, you’re doing so for emphasis, which is perfectly grammatically correct English.
It’s really a no-brainer.
Why not just, “Where are you going?”
Or, “Hell! That’s where I’m going.”
I’ve heard this in Saskatchewan by people of German descent.
Since you don’t know what prepositions are, you shouldn’t have a strong opinion (exceptions or no) about whether they should be at the end of sentences or not.
Well, remember let’s not make everything black and white. I don’t fully understand prepositions but it’s not fair to say that I don’t have a good idea. I’m not a grammarian but it’s not that difficult of a concept.
Why?
If it’s “not that difficult a concept” for you, why did you think “this” was a preposition? There’s really no ambiguity about that one. And you realize that it can’t just be compiled into a neat list, right? Depending on how the word is being used, it may be a preposition, it may be an adverb, it may be another part of speech.
It’s cleaner and more concise. Why add the “to”?
Because I’m not an expert, but I’m not clueless.
No, I did not know that it can’t just be compiled into a neat list.
Because ‘going’ can mean more of a state than an actual place. You answer “where are to going” with “to take a nap.” You answer “where are you going to” with “to my bedroom.” The dangling preposition denotes specific place or direction, which is what the questioner may be looking for.
Sorry… for which the questioner may be looking. 
The other reason you’d might want to use “where are you going to” is because it’s common English parlance. That phrase has 86.7 million hits on Google. It is actually up to you to explain why wouldn’t someone use that construction since it’s so freaking common.
Well, let’s look at one example: “oustide.”
He thinks outside the box. “Outside” is a preposition here.
I went outside. “Outside” is an adverb here.
Jake hopes to join Elwood on the outside one day. “Outside” is a noun here.
There is an outside chance he will make the team. “Outside” is an adjective here.