Every once in a while I come across an article discussing another microorganism that managed to become resistant to an antibiotic, and had had an "interesting experience" with it myself: in 1996 I managed to get myself infected with the Shigella flexneri bacterium (causing dysenteria...) and the medical lab provided me with a list of antibiotics the S. flexneri was resistant to; thus useless to take those type of medicines. That was then and in Peru. In the meantime, the MRSA can only be treated with vancomycin, and the Pneumococcus causing pneumonia is even found to be resistant to that. Imagine, since the invention to use penicillin as a medicine to combat infections, those bacteria "learned" to defend themselves against the whole list of antibiotics below: their adaptability is faster that our increasing knowledge about antibiotics. Makes you wonder who is smarter.

To kill the bacteria, yeast and fungi, there are several methods depending on the structure and physiology of the organism. I grouped them in accordance with the target site, from basic inhibition of their reproduction to interference with its physiology further down the line.

Prevention of DNA synthesis
Mitomycin C

Inhibition of RNA synthesis
Actinomycin D
Rifamycin B (and derivative Rifampicin)

Inhibition of protein synthesis
Streptomycin A
Tetracyclines
chloramphenicol/chloromycetin
cycloheximide
Erythromycin
Puromycin
neomycin

Interference with cell wall synthesis
Penicillin
Phenethicillin
Ampicillin (and Amoxicillin)
Carbenicillin
Cephalosporin C
vancomycin

Membrane transport disruption
Gramicidin A
Valinomycin
Nonactin

Polypeptide antibiotics, detergents
polymyxin (derivative polysporin)
colistin
bacitracin
subtilin

I know there are more antibiotics than the ones I mentioned (about 100 in total), but they have more or less the same biochemical fuction as one or more mentioned above, but I'd like to have a complete list, so please /msg me if you know any others and I'll add them.

The most useful sources were my Biochemistry bible from Stryer, General Microbiology written by Schlegel and my own memory.