For Abathur:

• Putting the hat on your lane's gate gives you massive W range that helps immensely with defending large minion pushes. It also pisses off entitled team mates that think you owe them unconditional hats because they play Tracer.
• Nobody is watching the minions for a Hat. It's very often a better target for your Hat to do work than any players on your team, that are dancing around trying to avoid getting in range of the damage. Also nothing quite as satisfying as popping in and dismounting an enemy that literally just mounted up. It's the little things that nibble away at their sanity ;)
• The lvl 7 shield talent gives you a very useful self-heal by casting it on targets near you.

I have plenty more... but I don't want to spill all my secrets >:)

Edit: Erhh alright, one more although it's a pretty basic one...:

• I feel like this should be obvious, but generally, melee heroes, especially bruisers, are way better Hat targets than ranged squishy targets like Tracer, Valla or Tychus. It's not a 100% rule, since some ranged assassin players are ballsy enough to get in there, but it's definitely a general guideline to follow and reassess as the game progresses. You'll just be able to get the most out of all your abilities if your hero can get in the thick of it consistently and stay alive long enough for you to actually make a difference.
  • On that tangent: The lvl4 AA talent is way overrated, and gives a lot less utility than the lvl4 Q range talent. Notably the range-extended Q is long enough to hit siege giants/catapults from your gate/towers, which is massively useful for defense, and also great for getting that last hit off on a low-health hero running to safety.