I read that there are over 30,000 denominations. At the same time, I have read that this number is a gross exaggeration.
How many Christian denominations are there?
I'll restate the comment that this is a hard question to answer because it depends on the definition of denomination and it's hard to count/find every single denomination in the world.
The number you state (30,000+) probably comes from The World Christian Encyclopedia, specifically 2nd edition published in 2001. They use the following definition:
A denomination is defined in this Encyclopedia as an organized aggregate of worship centers or congregations of similar ecclesiastical tradition within a specific country; i.e. as an organized Christian church or tradition or religious group or community of believers, within a specific country, whose component congregations and members are called by the same denominational name in different areas, regarding themselves as one autonomous Christian church distinct from other denominations, churches and traditions. As defined here, world Christianity consists of 6 major ecclesiastico-cultural blocs, divided into 300 major ecclesiastical traditions, composed of over 33,000 distinct denominations in 238 countries, these denominations themselves being composed of over 3,400,000 worship centers, churches or congregations.”1
The Center for the Study of Global Christianity also has statistics that align closely to this number (see #41 in the link-34,200 denominations in 2000).
On a Christianity Statistics article, updated March 2017, states that there are approximately 41,000 Christian denominations, but they also state:
This statistic takes into consideration cultural distinctions of denominations in different countries, so there is overlapping of many denominations.
The World Christian Database represents over 9,000 Christian denominations. This number is quite lower than 30,000 but it also doesn't say what who exactly is represented or who isn't.
On Wikipedia they list about 1,100 denominations (according to my count) but Wikipedia isn't official.
For more details on the breakdown of (30,000+) read this article (not a primary source).
Based on the statistics from the above article (last link above) and the Christianity Statistics article I graphed the recorded denominations by year and the projected number of denominations in 2025.
All emphasis is added by me