S - Corporations do sometimes pay income taxes in very specific circumstances. S-Corporations are pass-throughs and therefore don't typically pay income tax. However, there are at least two exceptions off of the top of my head:
1. Built in gains tax. If a C- Corporation acquires an asset and the asset appreciates while still a C Corp and THEN the c-corp elects s-corp status before selling the asset then the S-Corp must pay taxes on that gain at regular corporate tax rates. This is obviously designed to prevent someone from using an s corp election to wrongly get the benefit of preferential individual capital gains rates. (You can actually get out of this tax by proving that the appreciation happened after the S-election.)
2. LIFO recapture tax. Same idea. If a c-corp elects s-corp status and THEN changes it's inventory accounting method, it basically has to pay tax on that gain as if it was a c-corp.
You could say that in principle these are really C-Corp taxes, but no matter how you slice it, these are tax liabilities resulting from the filing of the 1120-S.