Dragons are susceptible to physical injury, especially those involving sharp metal-pointed spears or arrows as well as injury from blunt trauma.
The 4th in the Dunk and Egg novella series "The Princess and the Queen" by GRRM contains a vivid depiction of the damage a dragon can receive:
Hundreds fled in terror from her flames … but hundreds more, drunk or
mad or possessed of the Warrior’s own courage, pushed through to the
attack. Even at the apex of the dome, the dragon was within easy reach
of archer and crossbowman, and arrows and quarrels flew at Dreamfyre
wherever she turned, at such close range that some few even punched
through her scales. Whenever she lighted, men swarmed to the attack,
driving her back into the air. Twice the dragon flew at the
Dragonpit’s great bronze gates, only to find them closed and barred
and defended by ranks of spears.
Unable to flee, Dreamfyre returned to the attack, savaging her
tormenters until the sands of the pit were strewn with charred
corpses, and the very air was thick with smoke and the smell of burned
flesh, yet still the spears and arrows flew. The end came when a
crossbow bolt nicked one of the dragon’s eyes. Half-blind, and
maddened by a dozen lesser wounds, Dreamfyre spread her wings and flew
straight up at the great dome above in a last desperate attempt to
break into the open sky. Already weakened by blasts of dragonflame,
the dome cracked under the force of impact, and a moment later half of
it came tumbling down, crushing both dragon and dragonslayers under
tons of broken stone and rubble.
Another was killed with a spear to the eye:
Morghul, it is written, was slain by the Burning Knight, a huge brute
of a man in heavy armor who rushed headlong into the dragon’s flame
with spear in hand, thrusting its point into the beast’s eye
repeatedly even as the dragonflame melted the steel plate that encased
him and devoured the flesh within.
and another with an axe to the head:
Shrykos was the first dragon to succumb, slain by a woodsman known as
Hobb the Hewer, who leapt onto her neck, driving his axe down into the
beast’s skull as Shrykos roared and twisted, trying to throw him off.
Seven blows did Hobb deliver with his legs locked round the dragon’s
neck, and each time his axe came down he roared out the name of one of
the Seven. It was the seventh blow, the Stranger’s blow, that slew the
dragon, crashing through scale and bones into the beast’s brain.
Another was apparently killed, either with a crossbow bolt but more likely with a grapnel:
Several differing tales were told afterward of how and why the dragon
fell. Some claimed a crossbowman put an iron bolt through his eye, but
this version seems suspiciously similar to the way Meraxes met her
end, long ago in Dorne. Another account tells us that a sailor in the
crow’s nest of a Myrish galley cast a grapnel as Vermax was swooping
through the fleet. One of its prongs found purchase between two
scales, and was driven deep by the dragon’s own considerable speed.
The sailor had coiled his end of the chain about the mast, and the
weight of the ship and the power of Vermax’s wings tore a long jagged
gash in the dragon’s belly. The dragon’s shriek of rage was heard as
far off as Spicetown, even through the clangor of battle. His flight
jerked to a violent end, Vermax went down smoking and screaming,
clawing at the water. Survivors said he struggled to rise, only to
crash headlong into a burning galley. Wood splintered, the mast came
tumbling down, and the dragon, thrashing, became entangled in the
rigging. When the ship heeled over and sank, Vermax sank with her.
Out of Universe, GRRM intriguingly suggested that we may see a dragon-on-dragon fight at some point in the future;
Q. Can a stag kill a dragon? More to the point, could any animal kill
A. That remains to be seen, but perhaps...another dragon.