World Species

The real number of species is a vexed question. Not only is there a difference of opinion among authorities as to what is recognised as a full species, but also how many still remain undiscovered.
With birds and mammals the basic numbers are fairly straightforward as certainly most of the extant species have been discovered, although quite often new species are being found, even large ones, or research reassesses a taxa and grades it as a new species.
The question of subspecies is contentious in relation to including them in extinction data (There are about 27,000 subspecies of birds for example, which as isolated populations are more likely to and do go extinct, but leave the species itself extant. The exclusion of subspecies rank therefore underestimates and distorts extinction data.).
This is also the case with reptiles and amphibians who have not been so well researched as birds and mammals and the discrepancies are certainly much greater.
With respect to insects, spiders, bacteria, viruses and other small life forms quantification is a major problem as identification is still in its infancy relative to the vertebrates. Almost any guess as to total numbers can and has been made. The resulting figures dwarf vertebrate numbers and although they may indeed be based on reasoned argument their use inflates and skews extinction data without being verifiable most of the time.
Some world totals go as far as 50 million, but the assessment below is the one I can accept, bearing in mind the actual state of our knowledge.
In most cases when discussing recent and current extinctions only vertebrates are considered. While they are the most visible and obvious extinctions and easily collated, it should not be forgotten that a vast number of non-vertebrates may be going extinct undetected in the biotopic underground, not only reducing our biodiversity but potentially increasing the chances of further extinctions through their absence.
Please remember the limitations of statistics and the fallibility of those who use them.

Taxa	Described	Perhaps exist
Mammalia	5416	5450
Aves	9917	10000
Reptilia	8300	10000
Amphibia	5743	7500
Fish	28900	35000
Agnatha	114
Cephalochordata	23
Tunicata	2566
Hemichordata	106
Echinodermata	7000	14000
Insecta	950000	4000000
Arachnida	98000	166K – 600K
Myriapoda	12200	>85000
Crustacea	40000	150000
Onychophora	165	220
Mollusca	70000	120000
Annelida	15000	25K – 30K
Nematoda	25000	500K
Acanthocephala	1000	1600
Platyhelminthes	20000	80000
Cnidaria	9000
Porifera	5500	18000
Other Invertebrata	10573	20000
Bryophyta	16600	22000
Ferns and allies	12838	15000
Gymnosperms	930	1000
Magnoliophyta	258650	320K
Lichens	17000	25000
Fungi	72000	1500000
Bacteria	5422	400K – 1M
Cyanophyta	2371
Algae	35000	200K
Viruses	2000	400K
Protoctista	42540	600K
	1,786,000	8 – 9Million

Data partly taken from: http://www.environment.gov.au/biodiversity/abrs/publications/other/species-numbers/02-exec-summary.html#vertebrates