When printing parts most things you can do to improve strength will negatively affect quality. You will need to understand the application of the part to understand what extent you can go to for improving strength, and you should ask questions about how the part could be changed for easier printing. Communication and iteration between CAD and manufacturing should be two-way, not just "print this part for me". Makers Muse has a great video with most of the information listed here if you prefer visuals:
Filament Choice
One of the most important aspects of printing strong parts is filament choice. While PLA might be great for a router case, it's not going to work for a pulley.
PETG - by far the easiest high-strength filament to print. It's about as strong as ABS, and doesn't require an enclosure. Good options for PETG are Matterhackers Pro PETG, and Prusament PETG.
ABS - very difficult to print but very strong, and dirt cheap. If you have an enclosure, consider experimenting with ABS. Pretty much all brands of ABS are the same.
PC - fairly difficult to print, and expensive, but also the strongest filament you can buy. Blends such as PolyMax PC can provide the strength of PC with much easier print-ability.
Temperature
When printing parts for high-strength, you should print at the highest possible temperature (within the range provided by the manufacturer) that will still result in a quality print. If you can disable the print fan and still have the part print with acceptable quality, do it.
Layer Thickness
The thicker the layers the stronger the part. You should print parts at the highest possible layer thickness that will still be sufficient for maintaining the dimensions of the part. Usually 0.2mm is good.
Extrusion Width and Multiplier
Make sure your extrusion width and multiplier settings are well tuned for the filament you're using.
Infill and Wall/Surface Thickness
Infill is often the first thing newbies will bump up when wanting a stronger part, but you get diminishing returns past 35%. Generally, you will see bigger strength gains from increasing wall thickness.
Annealing
Annealing can be tough since it can warp or shrink parts, but if you're able to design a part with that in mind, it can significantly improve strength and rigidity.
Bed Adhesion
While bed adhesion is a non-issue with PLA, when you try printing PETG, ABS, or PC you're bound to have issues. Here are a few tricks for better bed adhesion:
PETG - not much first layer squish, use aquanet super hold hair spray and apply coats to the bed until it's tacky
ABS - more first layer squish than you would normally use, blue tape or hair spray will work
PC - don't know yet :)