During a zombie outbreak or full out apocalypse, military agencies would be a crucial asset to survival. Working in cohesion, they are a lethal destructive force capable of hunting down and exterminating zombie hoards. The price is the massive amounts of equipment, weapons and supplies needed to maintain them.
A country with a strong army will have a much higher chance of containing the spread of zombies, or destroying entirely, where as smaller armies may be forced to retreat, or overwhelmed.
Modern ground forces utilizing contemporary weapons, vehicles, and tactics would have little to fear from an outbreak at any stage, concentration, or quantity. The ability to rapidly deploy expeditionary forces, with accompanying armor, artillery, and complementary air assets necessary for transport and support means that very large, extraordinarily defensible positions can be set up in nearly any location in a practically ad hoc manner.
Individual small units of infantry personnel would have very little to fear from even large swarms of zombies, given the training provided and the weapon systems at their disposal. While the nature of the enemy would impose restraints on the effectiveness of maneuver warfare, the basic mission of a line units is not affected: "to locate, close with, and destroy the enemy by fire and maneuver, and to repel the enemy's assault by fire and close combat." The weapons available to the infantry company are suitable for repelling significant numbers of targets, especially those that do not fight back, evade incoming fire, take cover, or attempt to defend themselves; all of these things make existing infantry tactics more effective, not less.
Machine gun fire in particular would be an exceptional asset against crowds. Grazing fire alone would either destroy, incapacitate, or degrade the movement of large numbers, with individual riflemen and designated marksman capable of picking off individual targets with steady, deliberate fire. Current training and marksmanship already allows for such tactics, and troops are already trained to make shots to the head in cases where a target is not stopped by fire to center of mass.
Utility vehicles with mounted weapons would offer similar utility as a machine gun team, with much greater longevity, mobility, and survivability; the machine guns in typical use by militaries are as accurate as any service rifle, and - thanks to the relatively low rate of fire of machine guns - careful trigger control allows for single shots or very short bursts. Given that a single vehicle like a Humvee can carry many thousands of rounds, and that the gunner is in an elevated, protected position on a vehicle capable of moving fairly quickly, it's easy to see how such platforms could be used as incredibly effective force multipliers.
The same can be said of tanks. A hallmark of modern armored fighting vehicles, the M1 Abrams, carries four machine guns in addition to its main 120mm smoothbore cannon: a set of coaxial machine guns chambered in .50BMG and 7.62x51mm, and individually mounted .50BMG and 7.62x51mm weapons mounted atop the turret. With all weapons capable of being remotely operated by individual crew members from inside the turret, and with ammunition reserves totaling over ten thousand rounds, a single tank could operate as a bastion for a defensive line, capable of raking down targets with great precision in single shots and bursts, or by laying out a sweeping wall of lead.
Artillery platforms would be similarly useful, especially against large concentrations of undead targets. Airburst fuzed 155mm, delivered by single or multiple batteries, is capable of quite literally vaporizing entire crowds of unprotected targets in the open. Even those targets not destroyed outright are vulnerable to tens of thousands of high-velocity fragmentation that can trivially penetrate the skull.
Air assets with significant utility include both attack and assault helicopters, which extend both the effective footprint of infantry forces and provide them with powerful fire support at their destination.Air to ground antitank missile systems, metal augmented missile systems, rockets, and chainguns and rotary guns firing high explosive and fragmenting cannon rounds with kill radii measured in the meters for each round fired offer an attractive counter to large numbers of hostile targets. Cargo and assault helos alone could sustain an incredible operations tempo for individual infantry units even while engaged, delivering vast quantities of ammunition and supplies to troops in the field.
All told, the destructiveness of modern weapons and platforms coupled with the training provided to combat forces enables a scenario where it is difficult to envision a lack of efficacy against the undead.
The navy forces would be a vital asset to any country during a zombie crisis. Large destroyers and aircraft carriers are literally floating cities with the ability to stay at sea for weeks at a time with the ability to hold limited amounts of survivors. The naval forces could be used for search and rescue missions, reconnaissance and patrolling the boarders to keep possible infected refugees from landing ashore at uninfected areas.
During an attack scenario the navy would be used primarily for coastal bombardment, landings and as safe landing pads for aircraft.
Air Force effectiveness
During smaller classed outbreaks, the Air Force would be used for insertions and extractions and search and destroy missions. Modern bombers and helicopters would "vaporize" undead targets before the army moves in.
In larger outbreaks aircraft would more likely be used to bomb infested cities or collapse bridges to prevent the further spread of the infection. But in later stages the Air Force would focus it's resources to maintain their transportation assets (transport aircrafts) as airstrikes deemed innefective.