In the field of linguistics, we do not do what your English teachers did and tell you how to talk and how to write. Linguists aren't concerned with appearances; we find it far more interesting to study how people DO talk, because the actual realization of language is far more interesting than any prescriptionist could make it. Oh yes. Prescriptionists. They prescribe how they think language should be. We are descriptionists. We describe what is.
When it comes to the English language, the prescriptionists have some pretty silly notions about how we should be talking that not only make little sense, they often end up making simple speech so complicated that it's hard to understand. If we followed their rules, the sentence "That is worth living for" would end up having to mutate into "That is something for which living is worth." Gesundheit.
Language naturally changes with time. This is unstoppable. In fact, there are rules that predict how languages change, which is what helps us go back and reconstruct dead languages. It changes very regularly. We simplify in one area, but then find other things more complicated over in this other area, so another change takes place. And so on and so forth. It changes on the phonetic level--how we pronounce our language--and the grammatical level--how we construct our words and sentences.
The rulebook that people teach out of these days for grammar is in fact something that most teachers themselves do not understand. Ask them where it comes from and most of them won't know. It's just The Way Things Are Done. Well, that's all fine and good if there's a good reason.
But in fact, most of the grammar rules of today were created by a small group of educated men several hundred years ago who decided that English is messy (amen, brother) and that it needed some cleaning up. In their day, the language of science was Latin. Latin was praised as the most logical form of language; it was "pure" language, perhaps the language in which the brain worked (we know today all this is rubbish, although Latin is very beautiful). So they took some Latin rules and worked them into English to end up with silly rules like these two:
1. Don't split the infinitive.
In English, we use the marker "to" in order to signify that we are putting the verb in its infinitive form. This is because we have limited morphology--the prefixes and suffixes you put on words, like -ing, -ed, and -s. To use the infinitive, we say "to run," "to sing," "to pontificate." But in Latin, there is morphology (special endings on the words) that signifies the infinitive.
To Latin scholars this is an oversimplification, but let's give an example anyway. The root of the verb for praise, "lauda," never occurs by itself; it always ended with some suffix denoting its conjugation. To say "to praise," you would say "laudare." What we use the "to" for is the "re" part.
So when we split the infinitive like in the classic example, "to boldy go" (where "boldly" occurs between the verb "go" and it's infinitive marker "to"), this is actually impossible to do in Latin. They wouldn't say lauda[boldly]re but laudare [boldly]. There are languages which do insert the adverb into the middle of the word, but Latin is not one of them.
So not only does this rule not make any sense in English, the conditions don't apply. Why shouldn't we be able to "split" the infinitive? Plenty of other languages like ours do it. It doesn't affect our understanding of the sentence; and sometimes it actually makes the sentence more robust.
2. Don't end the sentence in a preposition.
This one makes equally less sense, albeit for different reasons. First we must understand what a preposition is. A preposition is a predicating unit that sets off a noun. A prepositional phrase, consisting of the preposition (e.g. "in") and the noun phrase it governs (e.g. "the house"), modifies other particles of the sentence in the exact same way as adjectives/adverbs do. In fact, more and more linguists consider them the same thing. Adjectives, adverbs, and prepositional phrases are all what we call "adverbials," meaning essentially something that modifies the sentence in some way by adding extra information. It is not part of the core of the sentence construction.
But wait! Some verbs always have a prepositional phrase after them. Such as "to look AT" and "to care FOR." In order to have any sort of object with the verb "to care for"--the who or what that is being cared for--the so-called preposition "for" must used.
The jury is still out in linguistic communities as to what the "prepositions" count as in these scenarios, but we know that they are not prepositions. Just like the word "face" can be either a noun or verb, these pre's (as we'll call them) are serving double duty as a sort of additional predicate unit, acting on behalf of the verb.
In a prepositional phrase, the preposition and the noun are bound together in a phrase, such as, "The cake was IN A BOX." It's all one chunk with the noun. But that is not true here. The sentence "She cares for Alfred" might tempt us to call "for Alfred" a prepositional phrase, but in fact the verb is basically two words: She[Subject] cares-for[Verb] Alfred[Object]. We know this because when we put it in the infinitive, we get "to care for." That "for" is hanging onto "care" like a lover because even though they're different "words" with a space in between, they function as one meaningful unit. It's a two-word word. (Like marriage...?)
Furthermore, this grammatical construction is in our linguistic history; it's not a new thing. Those of you who have studied German know all about the verbs that govern their own attachment: let's take "anrufen," to call someone up. "Rufen" means "to call." "An" means something like "to" or "on"--the translation isn't exact into English. If you call someone, you "ruft [them] an." In other words, you call on them or call to them; German just puts the "preposition" after the noun instead of in front of it. Like us, the Germans put this unit with the verb when it is in the infinitive (an-rufen) and it is considered a single word.
Our German brother does it; why shouldn't English? Once again, someone unthinkingly tried to carry these rules over into our language without fully understanding how English works in and of itself. You have to wonder if they even spoke English. Sometimes it's nearly impossible to avoid ending your sentence in a pre because it is supposed to be there!
In my first example, I used the verb "to live for" which has one of those pre's on it. But in some sentence constructions, the object comes first in the sentence (remember it's usually subject-verb-object in English). In those cases, the pre doesn't tag along because it's not a prepositional phrase, it's a verb particle. Nobody says, "For cake is worth living." That's like saying, "To the house is worth going." We say that the house is worth going TO and that cake is/isn't worth living FOR. In order to not end in a "preposition," we'd have to say, "The house is something to which it is worth going. The cake is something for which it is worth living." That's archaic at best (and now you know why) and arrogant-sounding at worst.
You have to let English be what it is going to be and let Latin, Greek, and any other language be itself as well. Rules do not carry over, because every language is unique and beautiful and discrete within itself. To treat one as though they must live up to each other's standards and rules is to treat that language as inferior. I don't find English inferior. It's good at some things and bad at others. All languages are. Various attempts have been made throughout time to make a perfect language, and you know what? They never are. You can't have both efficient brevity and perfect describability; both easy distinction between sounds and easy articulation of sounds. Every language chooses its own balance of all the different parameters, and we get to see the kaleidoscope of how they all turn out.
Why is English so messy?
Language always is, but English particularly so. This is because of the amount of outside influence that has affected English. For a long time, Latin and Greek were the languages of education and study, and so there is a lot of influence from those. When the Normans invaded England ever so long ago, they brought many French words into the culture as well. And with English becoming, for better or worse, one of the most common trade languages around the world, it is now being influenced by countless other languages and cultures all clamoring to have their say (pun intended).
If you're interested in the history of English grammar, English Plus is a short and sweet resource.