I doubt if there is really a definitive answer. There was some news a while back that said that English had added its 1 millionth word. This is still an interesting article.
Words are Spoken.
The question, "How many words are there in English?" is based on a misunderstanding of language. It is based on the false assumptions that (1) words are objects that someone creates and (2) stores in a published dictionary. Neither assumption is true. Words that are simply spoken but never published do not enter dictionaries. That does not mean that they are not words, for language is a spoken medium, not a written one. Fewer than a thousand of the world's 6800 languages have writing systems. If words were the things found in dictionaries, the majority of the world's languages would have no words!
In point of fact, all languages are equipped to produce however many words are necessary for communication either internally, by derivation rules (lawyer > lawyerly) and compounding (water + fall > waterfall), or externally, by borrowing from other languages. So, one answer to the question in the title is: the number of possible words in any language at any given moment is infinite, for there is no limit on the number of possible words in any human language. However, we may distinguish between possible and actual words, so how many actual words are there in English?
Dictionaries are Word Samplings.
Dictionaries are convenient samplings of a language's vocabulary at a particular time and place. The problem here is that every dictionary contains a different number of words. You can certainly pick up any dictionary and find out how many words that dictionary samples. Usually, the approximate number of words contained in a dictionary is mentioned in the introduction. But compilers constantly make decisions as to whether to include this new word or exclude this old word based on arbitrary criteria such as space limitations, their memories, their attitudes as to whether it is commonly accepted or archaic, and their success in finding published sources.
Words are Used at Particular Times.
Dictionaries try to be timely, so they sample words that their compilers consider current. It is difficult to ascertain the currency of a word since words used yesterday may not be used today. On the other hand, two or three people may use an archaic word no one else uses. I recall in high school using "whither," "whence," "thither," "thence," among my friends to the point that they became an integral part of my vocabulary. I can still use them correctly. (I impressed—and probably amused—one of my English professors at the University of North Carolina when I let one accidentally slip in a conversation with him during my freshman year.)
Think of all the words that have existed in the past but are no longer used: "spats," "isinglass," "antidisestablishmentarianism," "fro." We cannot say that these words no longer "exist" but only that they are no longer used. We are free to begin using them any time we wish and in writing historical works, they are used. In fact, we often encourage resurrecting archaic words in our Word of the Day feature for good reason.
Words are Used in Particular Places.
Dictionaries are convenient samplings of a language's vocabulary from a particular place. English words are used in Australia and England that are not used in the U.S. One of yourDictionary.com's Words of the Day was "prepone," the obverse of "postpone." We announced it as the birth of a new word, since none of us here could find any evidence of it in the U.S. and the Canadian reader who sent it in assured us that it was new in Canada. But we received 4 messages from readers in India, assuring us that the word has been in use in India for at least 40 years!
For our Word of the Day feature at yourDictionary.com, we even try to find regional words like "gazump", "daft", "smarmy" (England) and "dag", "billabong", "dinkum" (Australia and New Zealand) to emphasize this point. So, even if words "exist" in the English language, they may exist in one geographical location and not others. How do we count words like this?
Derivational Diversity. Suppose we needed a new verb and either borrowed or created "blunk" to suit the purpose. We have added one new word to the vocabulary of a segment of the English-speaking population, right? Well, what about "blunker" and "blunking" and "blunkable" and "blunkability" and "unblunkability" and "blunked" and so on which are immediately available to any speaker the moment they hear the word? Have you ever heard "unclickability"? It doesn't appear in any dictionary but if we can "click" a hyperlink, can't we talk about the "unclickability" of a dead link? Is it a word or not? Of course, it is but it will never be in a dictionary unless is picks up an unusual meaning.
How about these words: kohlrabian (person eating only kohlrabi), concarnivore (someone eating only dishes with meat in them), or pondist "someone who plays a pond as a musical instrument). There is absolutely no use for these words so they are never used. Does that mean that they are not words? Some words are simply "there", provided by rules of grammar. Some are spoken at a given moment and never spoken again. In fact, they are "there" whether they are used or not. How can you count them?
Do Words Exist at All?
This may surprise you. Dr. Language's career before he came to yourDictionary.com was based on arguing before the scientific community that there are no such things as words! His "Separation Hypothesis," now widely accepted in the linguistic community, claims that what we take as words are in fact two distinct phenomena-lexemes and morphemes. Lexemes are noun, verb, and adjective (adverb) stems like "word," "speak," and "friend." Morphemes are everything else, including suffixes like -y, -ness, -er, -ing, -ly and prefixes like re-, un-, anti-.
When we speak, we do not always recall fully-formed words from our mental word storage (called a "lexicon") but rather lexemes. Before we utter them we have the option of adding morphemes (suffixes and prefixes). When we choose "word" we may say "word," or, by adding affixes, "wordy," or "wordiness," depending on what we want to express. We say "speaker" by recalling "speak" and adding -er to it.
So what is the difference between recalling "speaker" and recalling "speak" + "er"? There are many differences between lexemes and morphemes but the most important one is that lexemes are always pronounced-affixes are not! Someone who runs is a runner, right? Someone who flies is a flyer. That is because run means "run" and "er" means "someone who" and when you put them together, runner should mean "someone who runs." But if this logic is true, what means "someone who" in "a guide?" Or "a cook?" Or "a cheat?" There are millions of such words across all languages reflecting a regular change in meaning but with no sound to account for it. Apparently, the meaning of a morpheme may be expressed without sound.
Another difference is that lexemes, nouns, verbs, and adjectives, refer to things in the real world ("word," "speak," "red") while morphemes refer only to grammatical categories like "Past Tense, Plural Number, Agentive (a runner, a cook). No language has an inaudible lexeme. Morphemes, on the other hand, seem to function just as well inaudibly as audibly. This means that when we utter what we normally think of as "words," the brain is actually carrying out two distinct tasks: recalling the sound and meaning of lexemes and adding (or not) something quite different, morphemes. Current evidence now suggests that the two processes take place in two different parts of the brain.
So speaking is not what it seems to be. We don't simply memorize the words we know in our mental lexicons and keep the remainder in published dictionaries. First of all, we can create words on the spot whenever we need them by the two-step process mentioned above. We can use a foreign word if everyone understands it, even if it is never used again and never appears in a dictionary.
Second, dictionaries are samplings of published words at a given time in a given place. Dictionaries exist only among the small minority of the world's languages with writing systems but all languages contain words (that is, lexemes and morphemes). Some claim that there are a half million actual words in English, others say there are a million, and still others claim the number is two million. All these numbers are dreamed up by the author of the claim have nothing to do with reality.
It is true that English borrows recklessly from virtually every language on earth. In fact, "borrow" may be too weak in speaking of English; we should say that English aggressively mugs other languages for their lexical treasure (see 'Words: Where do they Come from' elsewhere in the library for details). We might just as well claim that the number of English words is equivalent to the number of words in all the Earth's languages. That is as true as any other figure we could come up with by any means.
The very best attitude is to take another sip of your favorite wine, savor it with the words we have in our truly luxurious lexical storehouse, and never let the question in the title of this paper ever cross your mind again.
Anonymous. 2009. "How many words are in English?". Your dictionary.com. Available online: http://www.yourdictionary.com/library/How-Many-Words-Are-In-English.html