NY roof hook and TIC.  Along with personal tools kept in pockets, webbing, wire cutters, screw driver, folding spanner, shove knife and radio.  The TIC is of course to search for victims and/or fire during entry and help locate hot spots during overhaul.  The Roof Hook is for pulling ceilings or opening walls to check for extension.  As a volunteer department, typically the "truck work" is done by the same people pulling in the initial attack line so we may also take a haligan and TNT tool to force entry but normally they get left next to the door.

Depending on the day and the relative humidity, there is no telling what will get brought inside. If we're lucky someone remembers the TIC. Depending on which rig I pulled up on I will grab either the irons, or a hook and attic ladder along with an extra box light. We have a lot of guys who wait until they need something and then either run back to the rig or ask someone else to grab it. I get picked on for looking like a mobile tool kit, but that's what it takes when no one else is grabbing tools. 

I know about picked on. They used to call me inspector gadget, but they were always borrowing my tools.