You give the red USUALLY to the ADC because the ADC typically lacks a form of CC. Some ADCs also lack slows, i.e. Sivir. The slow helps the ADC kite a little bit better while they also are capable of putting the DoT to slightly more use.
Twitch and Ezreal typically put red buff to the most use with Ezreal's Q poke and Twitch's R, which procs on-hits to -every- champion hit, thus providing ungodly amounts of red buff havoc everywhere. Before you ask, no, Jinx's rockets do not apply red buff. Her rocket's AoE do not apply any on-hits or even lifesteal on anything other than the first target hit.
In some cases, Bruisers and tanks can put red buff to as much use as an ADC, especially when you have lots of peel for your ADC, but one of your bruisers lacks stickiness such as Shyv, Renekton, and Poppy who have issues when their target decides to use a dash to escape after they've used their own long CD gap closer to get close to begin with.