Super tight brakes don't work My son is at an age where I could be buying him a new bike each year because he is growing, but instead I managed to pick up a free bike from someone who put it out for trash collection.

Only problem is the brake pads were worn to the end.

I have replaced the brake cable, tried two different sets of different brand brake pads and tightened everything until it can't be tightened anymore.

You can see from the pics that the brake pads are right up against the rims, but those @&amp;$@#%s just don't stop the bike.

The pictures show the pads right up against the rims when the brakes aren't even engaged.

The only thing I can think is the rims. Any suggestions?
Reading the comments I am going to presume the problem lies with the rim/pad interface not generating enough friction rather than pressure from the brake lever getting to the pad/rim interface. 

First step - Presume the rim is contaminated with something slippery. Clean the rim presuming its either oil or silicon based. Use an degreaser/solvent first to attack an oil based contamination, the use an abrasive cleaner and scrub well with a steel wool or aggregative nylon scrubber and plenty of soapy water to remove non-oil based contaminants. Don't worry too much about damaging the rim - if you can't get the brakes working do you want you son riding on it? 

Now the pads - presume these, even if new, have been contaminated by the rims. Ideally buy new ones (Come to that later), second best and worth a try is to clean them with degreaser, soapy water then file or sand the top layer off. 

Assemble them with a bit of toe in (front of pad hits rim first). Put them together. (Look here for good instructions). Now the brakes need to bed in. Go for a ride, and give them a dozen of so max effort stops from high speed (careful you don't do anything silly) 

Couple of points: Are the pads good quality one like Koolstop?  Cheap pads are often made of hard compound, take a long time to bed in and have low friction.  If possible, get softer pads with more grip (and shorter life). The brakes are calliper brakes typical of road bikes, that offer poorer braking compared to V brakes and discs. Better callipers may help, but they do have a limit of how good they can get.