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The estimated number of species on Earth, as reported in this article is around 8.7 million. I am fascinated by how nature produces such a wide variety of species.

As per my understanding, many species have gone extinct, that is, were not able to adapt to changing conditions on Earth. Perhaps the number of species before few thousands of years were larger than today. Can we estimate the approximate number of species at a given point in the past, using available data?

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Nice question. It would be interesting to try and plot the extinction of species vs speciation of a new one. I strongly doubt it's liner over time, even if you account for catastrophic extinction events. –  Atl LED Aug 28 '13 at 17:03
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according to the National Science Foundation press release"Species Have Come and Gone at Different Rates than Previously Believed" indeed show what Atl LED suggests, that the progression is not linear, with the study showing that:

The previously thought exponential increase in diversity is not there.

Further, there is the "Palaeobiology Database, that

seeks to provide researchers and the public with information about the entire fossil record.

The site also has links to further papers of the topic.

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