Physical Constants
(taken from CODATA internationally recommended values: http://physics.nist.gov/cuu/Constants/index.html)
description letter variable Value (uncertainty)* relative uncertainty**
Speed of light in vacuum c 299,792,458 m s-1 exact
Planck Constant h 6.62606957(29) 10-34 J s 4.410-8
Bohr radius a0 0.52917721092(17) 10-10 m 3.210-10
electron mass me 9.10938291(40) 10-31 kg 4.410-8
elementary (electron) charge e 1.602176535(35) 10-19 C 2.210-8
Avagadro Constant NA 6.02214129(27) 1023 mol-1 4.410-8
Boltzman Constant k 1.3806487(12) 10-23 J K-1 9.110-7
Faraday Constant F 96485.3365(21) C mol-1 2.210-8
Molar Ideal Gas Constant R 8.314 4621 J mol-1 K-1 9.110-7
Rydberg Constant RH 2.179872171 10-18 J 4.4 10-8

Note that these values are quoted to a very large number of sig figs since the values have been measured quite accurately.  These values are periodically updated as better and better measurement techniques are developed.  The values quoted here are current as of 2012.  Any updates to these numbers will likely only occur in the last couple of decimal places so you can feel safe in using these numbers.

* The uncertainties quoted here are generally determined statistically as a result of multiple measurements by several researchers.  They are the statistical standard error.

** The relative uncertainty is simply the standard error divided by the actual value.  For example, the relative uncertainty for Planck Constant is calculated as follows

0.00000029 10-34 J s  = 4.4 10-8
6.62606957  10-34 J s

A good way to visualize the meaning of relative uncertainty is to look at the power of 10 exponent.  It gives roughly the number of sig figs in the numeric value. Hence, Planck Constant is known to about 8 sig figs. 

In first year chemistry, we generally use only 3 or 4 sig figs in our problem solutions.  So most chemistry texts don't even bother quoting the uncertainty in these physical constants.  These texts merely quote the physical constant to less digits (5 or 6) and the students are left to take these as being perfectly accurate.  Doing this simplification will not induce much error as long as the number of digits used in the physical constant is at least two more than the number of sig figs in the problem values.