A crossfire (also known as "interlocking fire") is a military term for the siting of weapons (often automatic weapons such as machine guns) so that their arcs of fire overlap. This tactic came to prominence in World War I.
Use of armour, air support, indirect fire support, and stealth are tactics that may be used to assault a defensive position. However when combined with land-mines, snipers, barbed wire, and air cover, crossfire became a difficult tactic to counter in the early 20th century.
Three things changed between WWI and WWII, rendering crossfire tactics obsolete: the advance of armored vehicles (especially tanks), the advent of aerial bombardment, and the invention of the proximity fuze.
Tanks were invented in WWI specifically because they were immune to machine gun fire, and could thus cross no man's land to destroy the machine gun nests. Their armored hulls also provided cover for the infantry to advance around the tanks. The tanks in WWI were ponderously slow and prone to stalling, however, so they tipped the balance in the favor of the British, but not decisively. In WWII, the tanks improved greatly in speed and reliability, and could reach a machine gun nest at reduced risk since it spent less time exposed.
Airplanes were present in WWI, but they were used primarily for recon and the outcome of the battle in the air didn't have a lot of effect on the ground battle. The pilots often experimented with carrying things like hand grenades to drop on the enemy, but they were largely ineffective. In WWII airplanes could bomb enemy lines, rendering any large stationary target vulnerable to destruction. Fighters also strafed enemy lines with machine gun fire.
The proximity fuze allowed bombs and munitions to detonate when an object passed within a certain range (usually about 50 feet (15 m)) rather than using an impact or timed fuze. Timed fuzes are tricky because the range has to be pre-set correctly. Impact fuzes are ineffective against flying targets because they have a very small targeting silhouette, and ineffective against ground targets because the projectile has time to embed in the ground before it explodes, deflecting the explosive power upward. Proximity fuzes were developed by the U.S. Navy during WWII, and they proved instrumental in defending the fleets from aerial attack since a gunner using bullets with proximity fuzes only had to get close to hitting the enemy to knock him from the sky. Proximity fuzes were also instrumental in the Battle of Britain. Their effectiveness against German air raids is demonstrated by the fact that, after the British flak batteries changed to proximity fuzes, not a single German bomb made it past the guns. The fuze also permitted the heavy artillery to detonate above ground, permitting the explosive power to be fully utilized against targets on the ground. The trenches of WWI, for instance, wouldn't have been effective protection against a bombardment using proximity fuzes.
Any of the above three technologies would have rendered the crossfire useless. Modern warfare has not returned to big blocks of infantry because the above inventions also kill massed infantry well; to survive heavy combat in the post-WWI environment, infantry must disperse into smaller, more independent units designed to take full advantage of cover and concealment. With the perfection of shoulder-launched rockets (such as the ubiquitous Bazooka) and precision bombing, stationary targets are too vulnerable to be as deadly as the crossfire was in WWI.