Currently I play with keyboard and mouse.
I have a controller, but I play most PC shmups and platformers with keyboard (and mouse if applicable) if it works decently. I'll usually try them with a controller to see if it works better, but usually I need to get a noticeable "performance benefit" for me to bother getting out the controller for that game after that, and for me that doesn't happen all too often.
Part of it is probably out of habit.
I started playing shmups by playing Touhou games during long waiting times between military-simulation-style ArmA missions. I typically used keyboard because I wouldn't have a gamepad hooked up at the time, so I got used to playing shmups with keyboard and the habit kind of stuck.
Honestly, I think the games my controller gets the most use for are the Dark Souls series, console-style action games like Metal Gear Rising: Revengeance, and driving games like Euro Truck Simulator 2.