"Who likes beans?"
"Mary likes beans."

"How does Mary feel about beans?"
"Mary likes beans."

"What does Mary like to eat?"
"Mary likes beans."

"Who likes beans?"
"MARY likes beans."

"How does Mary feel about beans?"
"Mary LIKES beans."

"What does Mary like to eat?"
"Mary likes BEANS."

As Cerberus hints in his comment on Aspinea's answer, it's quite common to use word order to convey information structure. (Sadly, Wikipedia doesn't have an article on the relevant sense of the phrase "information structure," and I can't find a good nontechnical introduction elsewhere. This article is a good survey of the subject for linguists.)

Information structure is a pretty broad subject, but there are two basic ideas that are especially important when you're talking about word order: topic and focus. The topic of a sentence is, roughly speaking, "what the sentence is about." Usually, a sequence of sentences will have the same topic, or at least closely related topics. But sometimes you'll want to change topics between sentences, or to contrast two topics with one another -- and speakers will tend to mark the new topic in some way when they do this.

English actually does mark topic changes using word order, at least some of the time. In passages like these...

...the left-dislocated word in the second sentence ("me" or "lentils") is marking a change in topic. "Okay, we were talking about beans before, but now we're gonna switch gears and talk about lentils for a while."

"Who likes beans?" "MARY likes beans."

"How does Mary feel about beans?" "Mary LIKES beans."

"What does Mary like to eat?" "Mary likes BEANS."

So lemme give some examples from K'ichee', which is a "free word order" language that I've studied for a while. Default word order in K'ichee' is VOS, so the standard way of saying "Mary likes beans" would look like this:

In K'ichee', both topics and foci can move to the left of the clause. After a topic, you get a pause; there's no pause after a focus; and if both the topic and focus move, the topic goes first. You can also move words to the end of the clause, which makes them sound a bit like an afterthought. So the "real" word order in K'iche' is more like "Topic (pause) focus V normal-O normal-S (pause) afterthought," though of course you won't get all those slots filled in a single clause.

(This changes the topic and answers a question. For instance, maybe you asked a minute ago about what someone else likes, but now you're asking what Mary likes, and I'm answering the second question)

(This makes "beans" an afterthought. You might use it when you've been talking on the topic of beans for a while, but you want to remind your listener that that's what you're talking about.)

And so on. The upshot is, all six permutations of subject, verb and object are possible in K'ichee', given the right combination of topic, focus and afterthought.

FWIW too, I don't speak Polish but it looks like something similar is going on in Kamil Stachowski's Polish examples. Note that sometimes he says that a particular word order answers a specific question. This suggests to me that those word orders are being used for focus-marking in Polish -- and a little Googling turns up this article on Polish focus-marking claiming that word order is indeed relevant.

As Cerberus hints in his comment on Aspinea's answer, it's quite common to use word order to convey information structure. (Sadly, Wikipedia doesn't have an article on the relevant sense of the phrase "information structure," and I can't find a good nontechnical introduction elsewhere. The article "Basic Notions of Information Structure" by Manfred Krifka is a good survey of the subject for linguists.)

Information structure is a pretty broad subject, but there are two basic ideas that are especially important when you're talking about word order: topic and focus. The topic of a sentence is, roughly speaking, "what the sentence is about". Usually, a sequence of sentences will have the same topic, or at least closely related topics. But sometimes you'll want to change topics between sentences, or to contrast two topics with one another — and speakers will tend to mark the new topic in some way when they do this.

English actually does mark topic changes using word order, at least some of the time. In passages like these...

...the left-dislocated word in the second sentence ("me" or "lentils") is marking a change in topic: "Okay, we were talking about beans before, but now we're gonna switch gears and talk about lentils for a while."

"Who likes beans?"
"Mary likes beans."

"How does Mary feel about beans?"
"Mary likes beans."

"What does Mary like to eat?"
"Mary likes beans."

So let me give some examples from K'ichee', which is a "free word order" language that I've studied for a while. Default word order in K'ichee' is VOS, so the standard way of saying "Mary likes beans" would look like this:

In K'ichee', both topics and foci can move to the left of the clause. After a topic, you get a pause; there's no pause after a focus; and if both the topic and focus move, the topic goes first. You can also move words to the end of the clause, which makes them sound a bit like an afterthought. So the "real" word order in K'iche' is more like "Topic (pause) focus V normal-O normal-S (pause) afterthought," though of course you won't get all those slots filled in a single clause.

(This changes the topic and answers a question. For instance, maybe you asked a minute ago about what someone else likes, but now you're asking what Mary likes, and I'm answering the second question)

(This makes "beans" an afterthought. You might use it when you've been talking on the topic of beans for a while, but you want to remind your listener that that's what you're talking about.)

And so on. The upshot is, all six permutations of subject, verb and object are possible in K'ichee', given the right combination of topic, focus and afterthought.

For what it's worth too, I don't speak Polish but it looks like something similar is going on in Kamil Stachowski's Polish examples. Note that sometimes he says that a particular word order answers a specific question. This suggests to me that those word orders are being used for focus-marking in Polish — and a little Googling turns up this article on Polish focus-marking claiming that word order is indeed relevant.