Why do we say "going on the train", "going on the bus" but we go "in" the car?

Probably because you typically crawl/climb into a car. You step onto a train/bus then walk to your seat.

I never thought of that @Silence04… Perhaps you are right…

Perhaps its similar to why we park in a driveway but drive on a parkway?

(with a nod to Steven Wright)

I agree with @Silence04. You climb into a car but step onto a bus or train carriage.

For the question at hand, I would suggest the following principles:

“On” is used when you ride on top of the transport, rather than being enclosed by it (on a bicycle, on a motorcycle, on a scooter).
“On” is also used when the vehicle is large (large enough to stand up and walk around) (on a bus, on a train, on a ship).
“In” is used when you are enclosed in a small vehicle (in a car).

Note that this means that for some forms of transport it’s possible to use both “in” or “on”, depending on the size: I personally would say on a Boeing 747, but in a Cessna, and I might similarly use both “in a boat” and “on a boat” depending on how large/enclosed I felt.

Also note that the above are not by any means strict “Rules of English” — they are based on how I (as a native speaker) perceive I use the prepositions. I’m sure there are exceptions, and I’m sure people will point them out — but this is probably a good rule of thumb at least for common cases.

Because English is a mess. I’ve said this before. Prepositions are one of the harder parts of the language to figure out, especially for ESL people.

In Spanish in and on are the same word “en.” Many people whose first language is Spanish, have trouble with in and on in English. The basic rule to help them is “on” is used as a short for “on top of,” and, “in” is a short for “inside of.” For instance, the shirt is on the table and the shirt is in the bag. There actually is a Spanish equivalent for “on top of” and so if the Spanish speaker knows that would be correct then they know to use on not in, except when the rule doesn’t work, like with things like trains and planes. Oy.

You can also travel “by” plane or train. Why does by make sense there?

Mostly, you just have to learn what is correct based on common usage and not jut the rules, because English has so many exceptions to so many rules.

Like I said, prepositions are difficult.

Because English is a silly language.

No, I’m serious. Think about how many different language quirks exist in the English language.

Since it’s nearly dinner time, let me put this one forward: Have dinner. In its various forms, it’s a little weird. “Have you had dinner?” “What are you having for dinner?”

Now, because I understand the language, I know that I mean “Have you eaten dinner yet?” or “What are you going to eat for dinner?”... But it is still an odd phrase.

We’ll Begin with a Box (Anonymous)

We’ll begin with a box, and the plural is boxes, 
But the plural of ox becomes oxen, not oxes.
One fowl is a goose, but two are called geese,
Yet the plural of moose should never be meese.
You may find a lone mouse or a nest full of mice,
Yet the plural of house is houses, not hice.

If the plural of man is always called men,
Why shouldn’t the plural of pan be called pen?
If I speak of my foot and show you my feet,
And I give you a boot, would a pair be called beet?
If one is a tooth and a whole set are teeth,
Why shouldn’t the plural of booth be called beeth?

Then one may be that, and three would be those,
Yet hat in the plural would never be hose,
And the plural of cat is cats, not cose.

We speak of a brother and also of brethren,
But though we say mother, we never say methren.
Then the masculine pronouns are he, his and him,
But imagine the feminine: she, shis and shim!

Let’s face it – English is a crazy language.
There is no egg in eggplant nor ham in hamburger;
Neither apple nor pine in pineapple.
English muffins weren’t invented in England.

We take English for granted, but if we explore its paradoxes,
We find that quicksand can work slowly, boxing rings are square,
And a guinea pig is neither from Guinea nor is it a pig.

And why is it that writers write but fingers don’t fing,
Grocers don’t groce and hammers don’t ham?
Doesn’t it seem crazy that you can make amends but not one amend?
If you have a bunch of odds and ends and get rid of all but one of them,
what do you call it?

If teachers taught, why didn’t preachers praught?
If a vegetarian eats vegetables, what does a humanitarian eat?
Sometimes I think all the folks who grew up
speaking English should be committed to an asylum
for the verbally insane.

In what other language do people recite at a play and play at a recital?
We ship by truck but send cargo by ship.
We have noses that run and feet that smell.
We park in a driveway and drive in a parkway.

And how can a slim chance and a fat chance be the same,
While a wise man and a wise guy are opposites?
You have to marvel at the unique lunacy of a language
In which your house can burn up as it burns down,
In which you fill in a form by filling it out, and
In which an alarm goes off by going on.

And in closing, if Father is Pop,
how come Mother is not called
Mop?

I have been convinced for a long, long, time that one of the functions of the English language is to confuse foreigners. This concept is quite Elizabethan, actually.

^^ And children ^^

English is a terribly confusing language to learn, but an extremely powerful as well as flexible tool for expression, nuance and description. And no language can match it when it comes to vocabulary and combinations. I strongly suspect that the “on” was carried over to planes and trains from the reference of being “on” ships. The expression “on” board is what makes me lean toward this conclusion. There’s little question that “boarding” a train or plane was carried over from the maritime tradition. And I too believe that the size of whatever is performing the transport matters. No one boards a rowboat or canoe, and though you may ride in a car, you ride on a bus. You may be “on” the train, but no one eats “on” the dining car or rides “on” one of the coaches. Speaking of which, before automobiles, with horse drawn coaches or carriages, “in” or “on” was specific. Think stagecoach to get the point.
It makes sense that when the trains and planes came along the maritime expressions would be carried over, and once you were ONboard, you were seated IN first class, coach, steerage, etc. So anything you have to “catch”, you invariably ride “on”. But it is confusing as hell if you haven’t grown up with the habit. Right now, I’m confused about whether or not you can catch a cab.

And then the Gaels got in there with slough, enough, trough, through, furlough… I’m just glad that I was born to this language and I admire anyone who speaks it well as a second one. I thought Swedish was tough!

I have no idea but my Latino girlfriend says “on” for all of them.

Lots of good ideas above. Me, I’m just a “travel by” kinda guy. Works with plane, train, car and bus.

@JLeslie and @Pachy: “by” used in this way is a bastardization of the word “via.”

I don’t know if it’s a bastardization, because I simply am not very knowledgable on the topic, but via makes sense as a synonym.

Why are some words that have the same ending, pronounced differently instead of rhyming?

Because English is a mess.

Which words are you thinking of?

It looks like we go “on the bus” or “on the train” or “on the plane” with strangers but we go “in the car,” a more personal experience, with people we know.