There is a variety of weapons used by Shadowhunters in The Shadowhunter Chronicles. Most of these weapons are made with materials capable of killing demons, some using adamas forged by the Iron Sisters.
Most used are the seraph blades, the primary weapons of the Nephilim. They are made of adamas crafted by the Iron Sisters. They call upon the power of an Angel's name to access the blade's power.
In addition to seraph blades, Jace also uses a sword, Alec alternatively uses a bow and arrow and a featherstaff, and Isabelle uses a whip in battle. Valentine used a kindjal, a Circassian dagger, in his first encounter with both Clary and Jace. Hodge Starkweather's, and Luke's weapon of choice were chakrams. Maryse Lightwood used a naginata.
The Sensor, invented by Henry Branwell, is a weapon that allows Shadowhunters to detect demonic energies. They can be fooled by Greater Demons, as Abbadon was able to keep his ethereal form just outside a portal be he attacked Jace and the others.
Shadowhunters are known to hide weapons in churches for their use in case of emergencies, since some forms of demons can only be killed and fought through a certain method of a belief systems. As long as Shadowhunters cleave to no single religion, all religions will assist in their battle. The weapons are usually hidden by a church's altar, with the Nephilim rune drawn over its hiding place.
Each species is weak to a certain element. Blessed iron is effective against fairies, silver powder and bullets against lycanthropes, holy water and other religious symbols against vampires, etc.