It depends on which Bible you use.
The number of chapters and verses in the Bible varies depending on which Bible you use. But just to keep things simple here, I'll refer to the King James Version (KJV) - 1611 A.D., (even though it too has been revised/updated 4 times), since it was the most popular, (albeit not the most understood), in the English language.
Although the newer translations are believed to be more accurate than the KJV, the differences are minor. No significant changes of belief or interpretation would result from the many minor corrections. The main advantage of the modern translations is that they are written in modern English so the reader will not be mystified or misled by the archaic English of the KJV.
The chapter and verses numbers were added a long time after the Bible was written (they were added to help people find their way around the Bible more easily. It is much easier to find "John chapter 3, verse 16" than it is to find "for God so loved the world..." ).
To answer the question...
The Bible is like a small library made up of 66 books. It has two big sections: the Old Testament and the New Testament. The Old Testament has 39 books, and the New Testament has 27 books. In most modern Bibles, in these 66 books, you will find a total of 1,189 chapters containing roughly about 31,173 verses.
How each book is divided up varies a little between translations and there are a few different numbering systems. For example, the Jewish verse numbering system of the Old Testament counts the titles of the psalms as verses, whereas usually the Christian numbering system leaves the titles unnumbered.
The number of verses can vary quite a lot as some verses are thought to be later additions and are left out of some translations, but this should give you some idea anyways!
Did You Know?...
Shortest book in the Bible: 2 John
Longest book in the Bible: Psalms
Chapters in the Bible: 1189
Chapters in the Old Testament: 929
Chapters in the New Testament: 260
Middle chapter of the Bible: Psalm 117
Shortest chapter in the Bible: Psalm 117
Longest chapter in the Bible: Psalm 119
Verses in the Old Testament: 23,214
Verses in the New Testament: 7,959
Shortest verse in the Bible: John 11:35
Longest verse in the Bible: Esther 8:9
Words in the Bible: 773,692
Words in the Old Testament: 592,439
Words in the New Testament: 181,253
Source(s): bibleqinfo.com/, gotquestions.org/, twopaths.com, discoverymagazine.com/