What is the largest wavelength that can excite an atom? What is the largest wavelength that can excite an atom? Or is there even a largest wavelength?
 A: It depends on the atom, the state it is in, and the definition of excite.
Here is the simplest atom, the hydrogen atom.

Normally the electron will be at the n=1 energy level. To get the electron excited to the n=2 energy level one needs a photon of energy $13.6-3.4=9.2$ eV, which gives a wavelength of $5.35*10^{-7}$meters. If  previously the electron has been excited close to the ionization energy level, the wavelength can be as large as the energy difference to complete ionization, a very large number as n goes to infinity in diminishing steps.
The same is true for all atoms, except the energy levels are different, unique for each atom.
A: An atom can be excited/ionized in a sufficiently strong electromagnetic field of arbitrarily low frequency through multi-photon excitation/ionization. I believe an atom can be ionized even in a sufficiently strong static electromagnetic field.
A: This depends on the atom. I assume you are interested in stable atoms only. I take "excite" as meaning that the atom is in its ground state initially. I am also assuming that forbidden transitions are allowed. Then my best guess is the Cesium 6s J=$\frac{1}{2} \rightarrow$ 6p J=$\frac{1} {2}$. The wave length is 894.3 nm. 
