In 1962 Toda published his book "Composition methods in homotopy groups of spheres", which contains computations of $\pi_{n+k}(S^n)$ for $k\le 19$ and $n\le 20$. The values of these groups are conveniently tabulated, and reproduced on the Wikipedia page Homotopy groups of spheres. The computations involve composition product, Toda brackets and the EHP sequence, as well as cohomology operations for the higher values of $k$.

I am fairly certain that more values of $\pi_{n+k}(S^n)$ have been computed in the intervening years, perhaps with more modern methods such as the unstable Adams spectral sequence.

Does anybody know of an up-to-date table of known unstable homotopy groups of spheres, beyond the range shown in Toda's tables?