
This is a tricky subject: games and movies are and should remain two distinct medium, and most techniques used to engage a viewer in a film don't suit game development at all. For this essay, let's consider that cinematic experience refers to how audio, visuals, narrative and gameplay can merge to create unforgettable memories. The term "cinematic" fits as these feelings were first triggered by movies and games tend to borrow techniques from films to reach similar goals.
Cinematic experience means immersion in a complex and active world, and all the other points of this essay actually contribute to the cinematic aspect of a game, but here I'm talking about the most striking, ultimate, the most cinematic moments of games. These moments when it seems that you've been sucked into your TV right into the middle of a scene and have to play your part.
However, don't mistake this for cut-scenes, which most of the time have little to do with a cinematic experience as defined here. Cut-scenes are simply short films interrupting the flow of the game, whereas the cinematic quality of a game is how close to playing a movie the player feels. Well directed cut-scenes can help develop the story and characters or show advanced scenes that couldn't be played, to add depth to the game world, but don't make a cinematic experience by themselves.
Games have become more influenced by movies, and it's important to think about what can be gained by this influence, and what will be lost if we're not careful. Some games are much more movie-like than others. Some of these movie-style games probably can incorporate certain cinematic techniques to good use. But games are their own unique medium, and [the] distinction [must be made] between good game design and good movie direction.
The most effective use of the cinematic aspect in games is usually to allow playing famous or common scenes that match closely their uninteractive counterparts. Kane and Lynch: Dead Men features many such scenes, like a gunfight in a nightclub à la Collateral.

Interestingly enough, witnessing events without being able to intervene in games also gives a movie-like feel to the experience, because of the incapability of the player to act on the sequence, but it doesn't rely on cutscenes, which would have been the closest to the movie experience. Taking only some control out of the player is an effective way of not breaking the flow of the game while giving this cinematic touch. The Brothers In Arms games use this trick with brio to convey the most dramatic scenes.

Techniques directly borrowed from movies that help nail the point are varied, such as the camera angles (Silent Hill series), multiple cameras like in Fahrenheit (The Indigo Prophecy) and Metal Gear Solid 4, or voice-over narrative.
I once had a chat with a gamer friend about memorable game experiences, and he instantly mentioned the ending of Metal Gear Solid 4 (shown below), how the events taking place on the upper screen, the desperate crawl of the player character, and the dramatic music left him with one of his best memories of gaming. What's surprising is that the only player interaction of this sequence is frantically pressing the action button.

After originality of settings, the originality of events or game features is a critical factor to wonderment. It sort of completes the point on game mechanics made earlier, but where a game mechanic blending in its environment helps immersion, these original sequences actually astonish by their novelty. These hooks can also help promote a game, for they intrigue and catch the attention of players.
I remember the buzz going about the realistic water effects of Metal Gear Solid 2: Sons of Liberty, about how they had placed motion captors in actual water to create the particles, etc. I couldn't wait to see it ingame.

It's like that first time you perform a shootdodge in Max Payne, that time slows, the pitch of sounds is reduced, and you can see the bullets fly around you. Or the first time you shoot a tree in Crysis and it breaks precisely at the point of impact and falls down. Or setting dry grass on fire in Far Cry 2 and seeing it progress, catching trees or foes. Or like the first kill in the first game you played that featured ragdolls, and watching the body of the enemy dropping realistically and bumping on the objects around it. Or the first time you saw realistic shadows in a game like Silent Hill 2.

The list is endless. The point is that new, groundbreaking features provide this Wow-factor I've been rambling about more easily than anything else, and games that don't have this to offer better use many other tricks of the book to distinguish themselves from the competition.

I grouped under this label the means of making an impression through grandeur (size, scale, multitude, distance, etc.) This includes landmarks, landscapes, huge bosses, armies, etc.
Landmarks are these structures that can be seen from almost everywhere in a level. They can be both impressive from the bottom, because of their scale compared to the player, or from the top, thanks to the view of the surroundings that they provide.
Landmarks are best if actually reachable: a landmark far away at the horizon that the player will never approach is still alright, but it's even more effective if the story eventually takes him there. We'd have been disappointed not to visit and climb at the top of the Citadel in Half-Life 2.

They can also serve as orientation aids, such as the tower of the central city of Oblivion, which can be seen from almost everywhere in the kingdom, informs the player about his own location simply by comparing its position to that landmark.

There's really little to say about landscapes and beautiful views: they're quite inspirational in real-life, so too in games if well depicted. It never hurts to have some of these panoramas in games, especially in contrast of an indoors sequence, like when exiting a cave.

As it was the case with landmarks, a great scale can give a character, object or structure lots of importance and have a powerful impact on players. We compare everything we see to our own size, so a gigantic cliff or a 4-meters-high enemy is bound to look impressive compared to a human game character. Shadow of the Colossus is probably the best example of the power of this technique, as most of the game's challenges consist in taking down enormous mythical creatures.

Another good illustration is the somewhat old game Giants: Citizen Kabuto, in which players control alternately human-sized characters and a giant monster. The levels played as the former are much more impressive than those played with the giant, because of the scale of the environment and enemies compared to the player-character.

In Call of Juarez: Bound in Blood, on many occasions the 2D mountains climb higher than the bottom half of the skybox. As a result, they look incredibly massive, and the fact that they slighly curve with the skybox's spherical shape, over the player's head, gives them a sort of 3D, in-your-face aspect.

Another instance of impressing through magnitude is to do so by the sheer number of characters at play. This is a known effect, important street riots always look impressive on the news, and many films touch their viewers that way, such as the Lord of the Rings movies or the ending of V for Vendetta.

It's become a major hook of Real-Time Strategy games to command real-sized armies of hundreds of units, like in the Total War series, but action-oriented titles also use this to a lesser extent, such as the Call of Duty games often putting numerous allies by your side to increase the scale of the assaults.

There are different ways to impress through scripted events, such as displaying paranormal visions, huge environmental and weather perturbations, beautiful particle effects, or combining that and having countless smaller events going on at once, like in most Call of Duty: Modern Warfare levels. This is probably the most varied category so far, as the possibilities are virtually endless.
A few notable instances of these can be found in Half-Life 2 and its episodes, witnessing the storm around the Citadel and the escaping combine pods while escaping from City 17 by train. In this case, the strength of the landmark is reinforced by the effects and events surrounding it.

In this creepy scene of Silent Hill 3, the player watches his avatar's reflection progressively rot and blood-like matter invade his own side of the mirror through a sink, to eventually suck the life out of her unless he exits the room in time.

The introduction of the Harbor level in Crysis features a battle between US and Koreans forces, with numerous explosions, firefights, and events such as planes crashing down in flames or dropping bombs. As a result, this is one of the most memorable sequences of the game.

These events, random or not (AI mobsters randomly chased by cops in Gran Theft Auto 4 compared to the scripted nuke explosion in FEAR), bring a level to life without having to take control out of the player like a cut-scene does. They should be used as often as they can enhance the game experience without confusing it more than intended. Players never get bored of beautiful effects as long as their use is justified, and the most impressive events will stay in the player's mind long after the game gets outdated.
Performing incredible actions as part of the gameplay is one of the most pleasing experiences in gaming. It relies heavily on the originality of the elements though (bullet-time was cool in the days of Max Payne, but lost its appeal along the way) but also on the quality of execution and realization: Tomb Raider's climbing & jumping was outdated, but has been revived by free-running in games like Assassin's Creed; and when killing enemies in FPS games got boring, ragdolls, pretty particles and realistic impacts helped keep the genre alive.

Besides being inherently part of the game's core gameplay, these moments can also be achieved through scripted sequences, such as this one in Call of Duty 4: the player, guided by his mentor, is infiltrating the whereabouts of Prypiat when they encounter a large enemy patrol, including heavy vehicles against which they are no match. Instead, they prone in the tall grass, and slowly crawl undetected at the feet of the enemies.

Fahrenheit is a game qualified as interactive movie, and in return for removing part of the freedom usually associated with gaming, it allows the player to perform amazing acts that remained thus far associated with the film domain (although most of them have been matched since by "normal" games, such as hanging on an helicopter in Gran Theft Auto 4 or bare-handedly taking out multiple armed foes in Batman: Arkham Asylum.)

These moments have much more impact on players thanks to their involvement and participation in the actions. Even if the process if facilitated (like to jumping around in Assassin's Creed requires little input) they'll remember it as being responsible for these cool scenes and cherish these experiences even more for it.