Pople Basis Sets
i) STO-3G  available for H to Cl
This is the well-known minimal basis set developed by Pople and coworkers in the early 1970s. Available are in the GENBAS file the sets for H to Cl, though in the literature also STO-3G sets for third-row and fourth-row main group elements as well as some transition metal elements have been reported.
The STO-3G basis is now more or less obsolete. Its use cannot be recommended for other than testing and rough preliminary investigations.
ii) 3-21G  available for H to Cl
This is a small "split-valence" basis set developed by Pople and coworkers. It uses a minimal (single-zeta) description for the core orbitals and a double-zeta description for the valence orbitals.
iii) 4-31G  available for H to Cl
The 4-31G set is similar to the 3-21G set, except that more primitive Gaussian functions are used.
iv) 6-31G  available for H to Cl
This is yet another split-valence set employing still more primitive Gaussians. Available for elements H to Cl.
v) 6-311G 
This is a split-valence set with a triple-zeta description of the valence orbtals and a minimal basis-set description of the core orbitals. Sets are available for H to Ne. It has been claimed in the literature [6-311g2] that this basis set is not really of triple-zeta valence quality.
vi) 6-31G*  available for H to Cl
This is the 6-31G basis supplemented with $d$ polarization function on all atoms except H and He. Note that this basis employs Cartesian polarization functions and should be used with SPHERICAL=OFF. The polarization exponents are Li (0.2); Be (0.4); B (0.6); C-Ne (0.8); Na, Mg (0.175); Al (0.325); Si (0.45); P (0.55); S (0.65); Cl (0.75).
vii) 6-31G**  available for H to Cl
The same as the 6-31G* basis except that the sets for H and He are supplemented by $p$ functions. The used exponents for H and He are 1.1.
viii) 6-311G*  available for H to Ne
This is the 6-311G basis supplemented with $d$ polarization functions on all atoms except H and He. Note that this basis has been especially developed for correlated calculations and (unlike 6-31G*) employs spherical polarization functions. The used polarization exponents are Li (0.2); Be (0.401); C (0.626); N (0.913); O (1.292); F (1.75); Ne (2.304)
ix) 6-311G**  available for H to Ne
The same as 6-311G* except that the sets for H and he are supplemented by $p$ functions. The used exponents for H and He are 0.75.
x) 6-31++G* and 6-31++G**