I'll just chime in with my experience using antibiotics in cell culture:
Generally, I have 3 types of antibiotics that I use: pen/strep, gentamicin, and fungizone (Amphotericin B). Penecillin/streptomyciin target gram-positive bacteria, gentamicin targets gram-negative, and fungizone goes after fungi. I use pen/strep and gentamicin constitutively, while fungizone gets used on an as-needed basis. I've also needed fluconozole for human cell culture.
I also have specialized antibiotics: kanamicin and G418 (geneticin).
All those antibiotics do different things: for example, pen/strep would kill my cells if used into high a concentration, while gentamicin simply cannot pass though the cell membrane. Similarly, fungi are more sensitive to fungizone than my cells, but if I use too much fungizone my cells would die as well.
When I transfect cells with, for example, a GFP fusion plasmid, the plasmid also contains a sequence that confers resistance to kanamicin (or geneticin). Thus, I can use kanamicin to select for transfected cells, as the wildtype cells get killed off.
Using pen/strep and gentamicin constitutively is not a good idea- I can help generate antibiotic-resistant strains of bacteria in the lab- but that's a trade-off many culture facilities consider when the environment is not as sterile as it should be. My lab and culture hood are in the Physics department, not the controlled environment of a medical research facility.
There is a very real problem of antibiotic-resistant bacteria in hospitals- partly due to the large amounts of antibiotics present, but also since the bacteria are near sick people. MRSA is one
http://en.wikipedia.org/wiki/Methicillin-resistant_Staphylococcus_aureus
as is tuberculosis:
http://en.wikipedia.org/wiki/Extensively_drug-resistant_tuberculosis
It's not clear how much all of the antibiotic-laden cleaning products used at home are contributing to the problem, but it's not zero.
Chemotherapy drugs are specific compounds that target surface molecules of rapidly growing cells: CD34, for example.
http://www.ebioscience.com/ebioscience/whatsnew/humancdchart.htm
However, 'normal' cells that also express these surface molecules (hair follicles, for example) are also killed off.