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?
同样,很难定义什么才算英语。医学和科学名词怎么办?法律中使用的拉丁词汇、烹饪中使用的法语词汇、学术写作中使用的德语词汇和武术中使用的日语词汇怎么办?苏格兰方言算不算?青少年的俚语呢?缩写呢?

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).
长达20卷的《牛津英语词典》第二版中有171476个仍在使用的单词词条,还有47156个废弃单词词条。此外还要加上约9500个派生词作为词条下面的分项。这些单词中,超过半数是名词,约四分之一的单词是形容词,七分之一左右的词是动词,剩下的是感叹词、连词、介词和词缀等。这一数字并未把单词的不同词性(例如名词和形容词)分别计算。

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.
这表明,英语中有至少25万单词,其中的20%可能已经不再使用。这25万单词中不包括变型、《牛津英语词典》中不收录的专业术语和地方方言、以及尚未被已出版词典收录的单词。如果要把同一单词的不同含义分别计算,英语单词的总数可能会接近75万。