Cutscenes have been getting a lot of flak lately, but if executed well they can create some of the best experiences in gaming. A good cutscene will get you pumped for the upcoming battle or mission and easily gets you in that ideal gaming "zone" where you're so into the game that your adrenalin kicks in. Have you ever finished a boss fight and found your hands shaking? And it felt awesome? That's what I'm talking about.
Sadly, games these days have a lot of missed opportunities when it comes to cutscenes. Pokemon actually is one of the better examples that comes to mind, specifically, the Giratina battle. For those of you who don't remember, this is what the Giratina battle was like. Not bad, to be honest, but if you consider that the battle could have started like this, it's not hard to see that a great opportunity was missed. The biggest difference between the two clips is that the second one builds up tension while you're waiting for the battle to begin and releases it all at once, just as it gives you the controls. The battle with Magus from Chrono trigger has a similar buildup, it has a feel sort of like an old style western showdown. In these types of cutscenes the choreography between the scene itself is massively important. The edited version of the Giratina battle wouldn't be remotely as epic if the music wasn't timed just right, or worse, if it were to simply have been the standard area music.
If we move outside of solid cutscenes we can consider events like the "battle on the big bridge" from Final Fantasy V, where the player has to fight through a series of battles in succession. Note that the music doesn't change when the battles start. Can you imagine how jarring it would be if every time one of the sub battles occurred the music changed to the combat music and then back to the event music when you finished? The battle on the bridge is supposed to be fast paced. By avoiding the music transition all of the battles can be strung together as a single event with minimal breaks in flow.
This almost feels like one extended battle.
We can also consider another option when integrating cutscenes and battles, which is the have the cutscene inside the battle itself. The series that best showcases this is the Breath of Fire (BoF) series. You would have to actually play the games to completely understand it, but Breath of Fire tends to inject the cutscene straight into the battle itself and there are occasions where the background actually comes into play in combat. In BoF 2 for example, Spar can use terrain elements to attack enemies. There are also some battles with special conditions, such as one battle where you only need to destroy the three guard robots and the game actually gives you a rather important vehicle later if you leave the main body of the boss unharmed.
So far, all of my examples have been RPGs. The biggest reason for this is because of the base design of an RPG's combat system. There is usually a very distinct point that the designer can use as a scene change, so they can time their music or dialogue around it. However, it is still possible to use a well timed cutscene in non-rpg games. Fatal frame is particularly good at this. Specifically with the one-time battles that occur such as when you enter an area for the first time and a ghost walks in front of the camera or drops down from the roof. In these cases, the game makes use of camera angles in order to create effects similar to those you would see in a good horror movie.
Now, that I've looked into what makes for a good story event. What makes one stale?
What first comes to mind is the case of the "talking heads" or in other words an extended dialogue cutscene that is just dialogue for the sake of it. Now, by itself, this is not necessarily a bad thing. However, if the cutscene is unskippable and long then it can wear on the patience of the player. Some people may simply not be in the mood for long dialogue sequences, or may have seen the sequence already. When a game has a large amount of these scenes it can chase off anyone who isn't a fan of the dialogue. That said, there are some people that like having long dialogue scenes, myself included, but there can be days where we just want to "get to it" and skip through to the action.
Another issue that stems from the "talking heads" cutscene is the static camera. If we consider the camera to be the window from which the viewer sees the game world, a lot of games have that window as a static one. A dynamic camera can help keep a player's attention because a static camera lets the player simply zone out during the cutscenes because a majority of the screen does not change. In addition to being an issue with RPGs this also extends to first person games. How many times have you gone to turn in a quest in Skyrim to think, "Yeah yeah, give me my reward already." *mashing advance* A lot of NPCs don't really DO anything but talk.
In fact Skyrim managed to break the mold a bit in the regard of interacting with NPCs, in the wilderness there are a lot of cases of running into NPCs fighting each other. A bandit being pursued by guards or something. I have to give credit to whoever came up with that concept for the game as it made journeying across the massive landscape much less dull.
Events in general have a lot of room for polish. To any developer reading this, even one epic cutscene can make a game. If you can manage to polish a cutscene to the point where it becomes an experience that sticks in the hearts and minds of the players, it may just push your game ahead of the pack.