Recently I found myself wanting to find the chart that gives the number of stars that can be seen brighter than a given magnitude. After some minutes of unsuccessful searching on the web, I decided to reinvent the wheel using data from HIPPARCOS. For those who may be interested, here are my results (where V is the limiting magnitude, and N is the number of stars brighter than V):
Magnitude (V) 
Number of Stars (N) 
Comments 
1 
1 
Sirus (1.44) 
0 
4 
Sirius, Canopus, Alpha Centauri, Arcturus 
1 
15 
Sirius,
Canopus, Alpha Centauri, Arcturus, Vega, Capella, Rigel, Procyon, Achernar, Hadar, Altair, Betelgeuse, Aldebaran, Acrux, Spica 
2 
49 

3 
172 

4 
507 
1/100 as bright as Sirius 
5 
1597 

6 
4977 
Limit of human eye 
7 
15373 

8 
45492 

9 
130400 
Visible in regular binoculars 
10 
360272 
Visible in 2 inch telescope 
11 
882935 
Visible in 3 inch telescope 
Beyond 11th magnitude, the Hipparcos data is incomplete. So to estimate the number of stars at fainter magnitudes, I plotted log_{10}N vs. V and did a secondorder polynomial fit to come up with the following empirical relationship between N and V:
N = 10^{(0.0064V^2 + 0.5589V + 0.5928)}
or, if you prefer:
log_{10}N = 0.0064V^{2} + 0.5589V + 0.5928
so to continue the table above by extrapolation:
Magnitude (V) 
Number of Stars (N) 
Comments 
12 
2387811 
Requires 1.2m telescope 
13 
5982738 
Requires 1.8m telescope 
14 
14554591 
Requires 3m telescope 
15 
34379535 
Requires 4.5m telescope 
16 
78849692 
Requires 7.5m telescope 
In other words, there are about 79 million stars brighter than 16^{th} magnitude.
Note that each magnitude step is 2.512 times fainter than the previous.
By comparison, the brightest planet Venus varies in brightness and is about 4.4 magnitude at maximum brightness, and Jupiter is about 2.2. The Moon is 12.7 magnitude at maximum brightness and the Sun is 26.75.
Adapted from a DomeL message posted by Chris Anderson of the Faulkner Planetarium and Herrett Centennial Observatory, January 2004