W is for 'We Have to Get the Bullet Out!'

'The doctors killed [President] Garfield, I just shot him.'
--Charles Guiteau
Once a character gets shot in Fictionland-- usually with a bullet, but sometimes with an arrow or other weapon-- it's a mad scramble by the team medic to get the offending object out of the wound.  I've already covered how TV first aid has an unfortunate tendency to become an instruction manual for the clueless and well-intentioned during an emergency, so before we analyse further:
If someone has been shot, stabbed, or otherwise punctured, DO NOT attempt to extract the object. 
The gunshot version of this trope actually has a reasonable origin. Before the invention of bullets, getting shot meant being punctured by a relatively large and slow-moving ball, which often tracked clothing or other debris into the wound. Getting the debris out reduced the chance of infection, and so was worth the other risks.
In modern times, however, the only circumstance in which one would want to remove an object from a wound is if the object itself is acutely toxic. Searching for an embedded bullet may cause more injuries than the original gunshot, and can also introduce bacteria or other foreign objects into the victim's insides. Similarly, removing something like an arrow or stick can cause additional damage on the way out. Plus the object in the wound is very likely acting as a cork, compressing tissues and blood vessels so that blood loss is minimised. With this plug removed, the victim will probably experience additional blood loss. 
If your characters must go pulling objects out of wounds-- they're doctors, they don't know any better, they're Kryptonite bullets, or they live in the 15th century and have no 'option B'-- that's fine. I'd suggest realistic medical complications where genre-appropriate, but go to it. 
However, I would once again seriously recommend first aid classes to anyone who can find the time. They are often free, held at convenient hours, and provide critical knowledge, even if you hope you never have to use it outside of writing your novel.