Proton torpedos, concussion missiles, thermal detonators. The Death Star has large wings of TIEs, including TIE Bombers which use all of the above. (And possibly other craft, like the Assault Gunboat. I'm told there's even a TIE Defender hidden in the rush of TIEs past the Millenium Falcon in RotJ, but I've never been able to find it for myself.)
It also has a large garrison force aboard, multiple divisions of Imperial Army troopers and stormtroopers. They make use of explosives: proton grenades, standard grenades, thermal detonators, probably whatever the Star Wars equivalent to plastic explosive is.