Most media (movies, video games, etc) portray the Tiger in idealized settings, such as one on one tank duels in an open field. This scenario is almost perfectly engineered to take advantage of the Tiger's strengths (powerful gun, thick front armour) while reducing its weaknesses (reliability, poor observation devices for the crew, ergonomics) as well as the weaknesses of the support chain for Tiger units.

Let's start with the gun-armour relationship. Many comparisons of the Tiger and its opponents boil down to "the Tiger could penetrate the front armour of some Allied tank from X meters, which could only penetrate the Tiger's front armour from Y meters, X>Y, therefore the Tiger is better". This evaluation misses the fact that tanks on a battlefield are not jousting knights. The battle begins before either of the opponents is aware of the other's location, and there are also many terrain features that keep them from firing at one another at long range. While it's possible to fire at an enemy tank from 2000 meters (there are many kill claims by Tigers at this range and even greater, but they are quite suspect), the actual engagement ranges are much smaller. Operational research found that 88 mm guns (this includes the higher velocity Pak and KwK 43) chiefly engaged their opponents from about 800 meters on the Eastern Front. Although Western Allied operational research doesn't filter out calibers specifically, the average range at which tanks were knocked out by artillery was about 800 yards in Europe and 900 yards in Africa. Italy was much shorter, at 350 yards. The Tigerfibel also calls to engage T-34s and Shermans at a range of 800 meters from the front, so let's say that a "typical" engagement is fought at 700-800 meters.

At this range the Tiger's gun can certainly penetrate the front armour of any Allied medium tank at 90 degrees, but its own armour is not impenetrable either. The front armour is vulnerable to Soviet 85 mm guns, American 76 mm guns, and British 17-pounders, all of which were available in ordinary medium tanks as well as purpose made tank destroyers. 57 mm 6-pounder and ZIS-2 anti-tank guns also had a fair chance against the front of a Tiger. In British trials even failures to penetrate resulted in the Tiger's armour cracking after several shots with AP. With HVAP or APDS ammunition most Allied guns were capable of penetrating the front of a Tiger.

The side armour can be engaged from an even longer distance. While it might be unfair to compare the engagement distance against the side, one must remember that tanks don't have perfect vision. Visibility from the Tiger was not great, the British noted that "it appears that the designers did not consider vision to be so important" in their evaluation of the tank. It was hard even for the commander to get a full view of the battlefield. He had to keep moving his head to get full coverage from each individual vision block of his cupola, not to mention switching from periscope to periscope. The position of the cupola and the fact that it was difficult for the commander to turn in his seat also led to significant dead zones, especially to the right and rear. The gunner's vision devices were also limited. He had an observation slit for looking left and a gun sight, but nothing aside from that. This meant that even if the Tiger's commander noticed an enemy tank and alerted his gunner, it would take some time for the gunner to acquire the target. British tests of a captured Tiger showed that it was also quite difficult for the gunner to traverse the turret, both with the powered traverse and the manual traverse. In case of the former, the traverse pedals were poorly located and hard to control, plus the traverse was very imprecise. In case of the latter, it was hard for the gunner to grasp the traverse flywheel comfortably, and the fact that the long gun made the turret out of balance made it difficult to turn. The commander's auxiliary flywheel didn't help much, since if used the gunner had great difficulty keeping the safety button on his own flywheel pressed as it began to rotate at a great speed.

As Allied tanks gave their gunners rotating periscopes, this handoff could happen much quicker. Noticing the enemy first also gave a great advantage, as if the conditions were unfavourable the tank could simply disengage or fire something other than AP (such as white phosphorous to blind the tank or trick the crew into thinking that it's on fire, HE to disable vision devices, etc).

A shot also doesn't have to punch through the tank's armour in order for it to be effective. Any gun in the Allied arsenal could knock out a Tiger's running gear. Recovery of a Tiger was not an easy thing. It took three unarmoured engineering halftracks, which made recovery impossible if the disabled tank was kept under artillery fire. Towing a Tiger with another Tiger was not recommended, as this commonly resulted in damage to the tank's transmission and lead to the loss of both tanks. Crews either had to risk this or improvise, for instance in Italy two captured Shermans without turrets were used to tow Tigers. This kind of weakness was known to the crews, and as the British noted Tigers that came under even slight artillery fire would choose to retreat rather than risk having their vehicles disabled and permanently lost. The tanks also tended to break down jus from driving, the ORO report I mention above estimates that 48.1% of German tanks were lost to noncombat damage (again, no filtering for Tigers). Air filters were quite poor, which lead to premature wear of the engine, and I already mentioned the strain to the transmission during normal operation.

There were also "one in a million" trick shots that resulted in catastrophic damage from unexpected weapons, for instance it was possible to ricochet a shell off the gun mantlet and punch through the fighting compartment roof or hit above the tracks but under the pannier floor and detonate the ammunition stored in the pannier. These are mentioned in proving grounds trials but naturally would be hard to pull off in combat.

It's worth talking about the quality of the Tiger's armour. On paper it's quite impressive, in reality it was somewhat less so. Soviet metallurgical examinations of samples obtained from Tiger tanks did not actually correspond to German metallurgical standards. The hardening process was also often incorrectly performed, leading to a vast range of behaviours under attack, most notably a tendency to crack and flake. British testing also found this property in German tanks. It is often said that the quality of German tank armour dropped in 1944-45 due to bombings of factories and declining supply of strategic alloys, but trials of tanks captured in 1943 showed the same brittleness and inconsistency.

Finally, tanks aren't the only enemies of a tank on the battlefield. Anti-tank artillery exists and can engage from an ambush at much closer ranges than a tank can, plus indirect fire artillery can shell parked tanks. Ground attack aircraft were also effective at harassing slow moving enemy tanks, although air attack was much more useful at dispersing formations than knocking out individual vehicles. Since the mobility of Tigers on soft ground severely limited the places they could drive through they were very vulnerable to anti-tank mines.

In conclusion, the Tiger was indeed a deadly opponent for most Allied tanks in the right circumstances. However, the tank's great mass, poor off-road performance, and low reliability made getting into those circumstances very difficult. Even if Tigers could be kept in fighting shape and get to the battlefield, there were a lot of factors that prevented them from lazily picking off Allied tanks at great distances like fish in a barrel. Guns that could defeat a Tiger at typical fighting ranges were already in production when the Tiger reached the battlefield, and even tanks armed with smaller guns could successfully engage their opponents with either skillful maneuver or specialized ammunition.

Sources:

http://www.tankarchives.ca/2013/08/combat-performance-of-75-cm-and-88-cm.html

ORO-T-117 Survey of Allied Tank Casualties in WWII

School of Tank Technology Report "Attack on Panther PzKw V and Tiger PzKw VI" April 1944

https://warspot.net/156-tiger-killers

http://www.tankarchives.ca/2018/04/tiger-air-filters.html

Military Operational Research Report No.61 Study No.11 Motion Studies of German Tanks.

So one thing about the Tiger, it's a heavy breakthrough tank designed in the old Blitzkrieg ways of punching holes in enemy lines and opening them up for exploitation.

For this, it was designed from the start to have very thick armor from the front, and a powerful gun that had a multipurpose ammo loadout to deal with infantry and bunkers, and other things the commander would like to see gone.

It was around the time the Tiger H1 went into general service that the Germans discovered the 88mm Flak gun in its emplaced and vehicular mountings were very strong against tanks like the British Matilda and Soviet KV series tanks, and also there was an increase in lethal range against other tanks like the M3 Lee/Grant tanks in the deserts of North Africa.

Luckily, this early showing also gave the Allies lots of lead time to get over the initial shock and develop counters to it in the earlier stages of the war. For instance, the US was already very satisfied with its 3-inch-gunned M10 GMC, which we used as a tank destroyer, contrary to popular belief, the 3 inch gun could penetrate the Tigers frontal plate at close (but not suicidally close) range. The M18 Hellcat GMC and its 76mm had good firepower and mobility on its side. The British found good use in the towed 17-pounder which eventually found it's way shoehorned into an M4 Sherman. The Russians pressed the 85mm gun into service which was comparable to the Tigers 88. Infantry was trained quickly in the new type and by Normandy and Operation Bagration in 1944, the Tiger was just a shadow of its former, feared self. The Panther, that's another story, and not related to the question.

The portrayal of a Tiger being a vaunted enemy, killing waves of enemies is mostly fact. When it was introduced a lot of tanks that enjoyed relative safety on the allied side suddenly were outmatched. Usually in movies this is done to show German dominance in as short a time as possible, like the Tiger battle in Fury. Once you sent a platoon of tanks to their demise a smart commander would think up something else.

For Logistics, the Germans for about 5 years enjoyed unparalleled air superiority and mostly open rail logistics. Most if not all heavy German vehicles relied on rail transport. The Tiger had special tracks fitted to allow it to fit through narrow railroad tunnels in Europe. Once the allies invaded France and started pushing closer to the fatherland, air superiority was wrested from the Germans and fighters returning from bomber escort would use their remaining fuel to strafe german trains, and bombers would also regularly target railyards and hubs throughout France and occupied Europe. By the beginning of 1945, more Tigers and Panthers had to be driven to their operational areas, which increased wear and corresponding chances to break down. That's not to say none made it to fight, many did. But by the end, with their industry a shambles, tigers were quite rare.

TL;DR The portrayals are accurate for early and mid war, by late war they were so rare that it was more a shock to see one working let alone fight one. Emphasis on rail transport hurt in the end.

Multiple sources here, some from Zaloga's Armored Thunderbolt and various works by Jentz and Doyle on German Armor in WWII.