Originally in response to a Quora question, I wrote down a list of constants that I need/use often, trying my best to remember them (not always successfully):

• $c\simeq 3\times 10^8~{\rm m}/{\rm s}$ (speed of light),
• $G\simeq 6.674\times 10^{-11}~{\rm m}^3/{\rm kg}\cdot{\rm s}^2$ (Newton's constant),
• $h\simeq 6.626\times 10^{-34}~{\rm m}^2{\rm kg}/{\rm s}$ (Planck's constant),
• $\alpha\simeq 1/137.036$ (fine structure constant),
• $\theta_W\simeq 0.231$ (Weinberg angle),
• $M_\oplus\simeq 6\times 10^{24}~{\rm kg}$ (mass of the Earth),
• $R_\oplus\simeq 6.37\times 10^6~{\rm m}$ (Earth radius),
• $M_\odot\simeq 2\times 10^{30}~{\rm kg}$ (solar mass),
• $1~{\rm AU}\simeq 1.5\times 10^{11}~{\rm m}$ (astronomical unit),
• $1~{\rm ly}\simeq 9.46\times 10^{15}~{\rm m}\simeq 10^{16}~{\rm m}$ (lightyear),
• $1~{\rm pc}\simeq 3.26~{\rm ly}\simeq 3.09\times 10^{16}~{\rm m}$ (parsec),
• $H_0\simeq 70 {\rm km}/{\rm s}/{\rm Mpc}$ (Hubble constant),
• $m_e\simeq 511~{\rm keV}$ (electron mass),
• $m_p\simeq 938~{\rm MeV}\simeq 1~{\rm GeV}$ (proton mass),
• $1~{\rm eV}\simeq 1.6\times 10^{-19}~{\rm J}$ (electronvolt),
• $R\simeq 8.314~{\rm J}/{\rm K}\cdot{\rm mol}$ (ideal gas constant),
• $\sigma\simeq 5.67\times 10^{-8}~{\rm W}/{\rm m}^2{\rm K}^4$ (Stefan-Boltzmann constant),
• $1~{\rm kiloton}=4.184\times 10^{12}~{\rm J}=10^{12}~{\rm cal}$ (TNT equivalent),
• $5.068\times 10^{4}~{\rm cm}^{-1}\simeq 1~{\rm eV}$ (natural units).