There is no single sensible answer to this question. It's impossible to count the number of words in a language, because it's so hard to decide what actually counts as a word. Is dog one word, or two (a noun meaning 'a kind of animal', and a verb meaning 'to follow persistently')? If we count it as two, then do we count inflections separately too (e.g. dogs = plural noun, dogs = present tense of the verb). Is dog-tired a word, or just two other words joined together? Is hot dog really two words, since it might also be written as hot-dog or even hotdog?
这个问题并没有一个简单而合理的答案。想要计算一种语言里有多少单词是不可能做到的,因为很难定义究竟什么才是一个单词。Dog究竟算一个单词还是两个(名词指一种动物,动词指长期跟随)?如果算作两个,那么我们是否也要把它的变型也单独计算(例如:复数名词dogs,第三人称单数现在时dogs)?Dog-tired(筋疲力尽)算一个单词还是两个连在一起的单词?既然Hot dog(热狗)可以被写成hot-dog甚至hotdog,它真的算两个单词吗?

It's also difficult to decide what counts as 'English'. What about medical and scientific terms? Latin words used in law, French words used in cooking, German words used in academic writing, Japanese words used in martial arts? Do you count Scots dialect? Teenage slang? Abbreviations?

The Second Edition of the 20-volume Oxford English Dictionary contains full entries for 171,476 words in current use, and 47,156 obsolete words. To this may be added around 9,500 derivative words included as subentries. Over half of these words are nouns, about a quarter adjectives, and about a seventh verbs; the rest is made up of exclamations, conjunctions, prepositions, suffixes, etc. And these figures don't take account of entries with senses for different word classes (such as noun and adjective).

易词解词(BY 摩西)

Oxford n. 牛津(英国城市)。要说“牛津”这两个字的翻译真是传神,ox是牛,而ford是浅滩和动词的涉水而过。牛津这地方本有一条小河,但水流不深,拉着牛车可以跋涉而过,故得名。有意思的是,这个ford是日耳曼词源,同德国城市法兰克福Frankfurt中的furt,Frankfurt,法兰克人的渡口之意。与希腊拉丁词源的port-词根表港口、搬运同源,于是airport,import,export,portal这些就好理解了。

quarter n. 四分之一;地区;季度;一刻钟;两角五分;节。拉丁词根quadr-,quart-表四分之一/第四,quart夸脱是四分之一加仑,quadruple是四倍的(ple-表fold倍数),quarantine检疫;隔离,是历史上欧洲黑死病期间进入威尼斯港口的船舶需要在港外停留40天观察有没有携带病菌,下次你要是看见某辆车的进气栅处有QUATTRO的字样,那它就是一辆四轮驱动的车。

This suggests that there are, at the very least, a quarter of a million distinct English words, excluding inflections, and words from technical and regional vocabulary not covered by the OED, or words not yet added to the published dictionary, of which perhaps 20 per cent are no longer in current use. If distinct senses were counted, the total would probably approach three quarters of a million.