While a lot of thrillers deal with the action/shoot-em-up conflicts and kind of bypass the rest, 24 manages to squeeze in a variety of other conflicts as well. It's awesome.
Jack and his colleagues not only fight terrorism but have to deal with personal conflicts between coworkers and loved ones. Jack and the president of the United States get identity conflicts. Two characters get in a romantic conflict. Others get into nature conflicts with illness, fatigue, and surgeries. The writers of 24 layer on lots of conflicts and all different kinds of conflict. I love that.
Even the terrorist conflicts vary. Jack has to break someone out of prison. Jack has to work under cover. A worm infects the computers at the Counter Terrorist Unit and so on.
So try mixing it up in your story. Throw in a romantic conflict in your thriller, an illness in your superhero story, or a question of identity in your comedy piece. Stack them on top of each other. Play with cause and effect. Too often we get stuck on writing one kind of conflict.
One of the most interesting, random conflicts that came up in 24 was when a character brought a baby to the Counter Terrorist Unit. While everyone is working to fight terrorists, there's this baby they have to take care of. Later we find out that the character who brought the baby to work (against work policy of course) isn't even the baby's mother, so now we're trying to figure out who the parents are. So we have all these little baby conflicts going on while Jack's trying to defend the United State of America. It's interesting, and helps keep the show fresh.
Look for opportunities to vary your conflicts. Maybe even try throwing something seemingly random in there that affects the plot, like that baby.