One of my favorite aspects of SW:TOR and Marvel Avengers Alliance is the ability to still advance my account even while not playing. Even if I don't play for an evening, I could still send characters to perform off-screen quests and actions. Obviously, you don't advance nearly as much as you would by playing live, but it's still a nice way to feel like you're not missing out due to a busy life.
What if we could do the same with our combat pets? Sure, your fierce combat rabbit probably can't take on a Sha by itself, but it could fetch Herbalism components. Maybe a mechanical pets could retrieve Engineering parts. Heck, maybe they'd just train up in the stadium. What do you think? What would you like to see your pets do while you're busy at work?