The element with the most protons discovered so far is ununoctium (Uuo, z=118) which is all the way over on the right side of the seventh period (a noble gas). So the natural question arises: what will the table look like when (if?) further elements are discovered? Wikipedia visualizes one possibility for an extended table (click to see larger version):
There are apparently a ton of caveats about this: (a) no one is sure in what order the orbitals are filled, and (b) the very concept of orbitals starts to breakdown above z=137 (Feynmanium) or z=173 (if you realistically model the nuclear force). To say nothing of that fact that these future elements may not be stable long enough to be observed (although many predict an Island of Stability around z=126).
Apparently the extended periodic table was first sketched out by Glenn Seaborg, and this talk shows a more familiar 'stacked' version of the extended table. Anyway, cool stuff I hadn't seen before.
(Apropos: I stumbled across this topic while researching Maria Goeppert-Mayer for work. MGM is the only other female Physics Nobel Prize winner, after Marie Curie. She did ground-breaking work on the shell model of the atomic nucleus while a researcher at Argonne National Lab. Like most pioneering female scientists she encountered just a stupid amount of sexism during the start of her career. Thankfully she stuck it out.)