This topic is based on my experience playing RPGs - mostly Japanese, granted, but it applies across the board. I have observed that turn-based or somewhat turn-based RPGs tend to have three different high level strategies. In fact, I'd go as far to say that all three should be supported. I'm going to call them "Just tank it", "tricks and deceit" and "kill him first". Although the names are pretty self-explanatory, there's a bunch of details concerned I'd like to discuss. They are applicable when the player encounters a fight they cannot outright win. This usually implies a boss fight, so for brevity's sake I'll be talking about them.
1. Just tank it
This is a very traditional approach. The concept is really simple: if the boss does too much damage for you to handle, grind levels until you can handle it. Handling it can mean a couple of different things, depending on the game's exact mechanics. Either having high enough defense and hit points to last the entire fight, or having powerful enough healing abilities to keep up with the damage. Typically a mixture of both since more defense means less healing. The purpose is not just to survive, but to actually negate all threat from the attacks - i.e., there is simply no way to lose. It's the safest way to go and it always works (well, unless the boss is designed to be challenging for maxed out characters - hello Atlus!) but it's a really really boring way to go. It sucks all the fun out of the boss fight. Oh and it involves all that grinding.
If this strategy is the only one supported in a game, that game is going to suck. It typically means the game is too simplistic and doesn't allow any actual combat tactics. This can also be a syndrome of too resilient bosses - when fights go on too long, using other strategies might not be feasible. So there's yet another reason to avoid designing boss fights that drag. It can also happen a lot with bosses that use nothing but area of effect attacks that hit everyone (and cannot be prevented). Although this strategy is boring, it still needs to exist in games. It's a useful fallback strategy, especially for less experienced players. The emphasis is on the word fallback. Designers should take care to incorporate the next two strategies as possibilities in their games.
2. Tricks and deceit
Incorporating this strategy in a game means offering the player all sorts of means to gap differences in power level. This can mean a myriad of things. Protective spells fall under this category as do various immunities. Games often provide abilities to become temporarily more resistant or offer more resilience as a tradeoff. Protect (FF series) is a standard issue example, a spell that halves physical damage. One-time immunity to a given element in Digital Devil Saga is another good example. The effectiveness of defensive tricks is often but not always dependent on the boss. Most importantly this typically means that the player needs to tailor his defensive tactics against each boss individually. By doing this a lot of grinding can be avoided. Even when the player does not have access to the abilities, there's often a lot less grinding involved in obtaining one ability than overleveling the entire party.
Instead of defensive tricks, players can also employ all sorts of measures that prevent the enemy from attacking. This gets especially intriguing if the boss can one-shot the entire party if it gets just a single turn. Although bosses often are immune to most debilitating status effects, they should not always be. This is actually what's led me to believe that status effect spells are useless in many RPGs - now I'm pleasantly surprised to find a boss that's not immune to everything. Negative effects are not the only way to go though. Some games have abilities that allow the player to delay their enemies' actions or make them miss a turn. Although we're now mostly talking about turn-based or similar games, stagger in real-time combat systems also falls in to this category.
The correct way to go about involving tricks in the game is to avoid too broadly applicable ones. Using them should always involve creativity from the player. It is always satisfying to complete tough battles in creative ways with characters who are way out of their league. This is what makes hardcore RPG fans play all sorts of crazy challenges where typically the first strategy mentioned here has been forbidden to a ridiculous extreme (e.g. no leveling up at all during the game). The need for tricks also often comes up when playing a game in an accelerated fashion, skipping a lot of leveling up possibilities and resources. Sometimes though, a boss is immune to all sorts of trickery and his attacks cannot be defended against. That's where the third strategy comes into play.
3. Kill him first
The name really says it all. If your healers cannot keep up with incoming damage, sometimes it's best to not heal at all and focus 100% on offensive. This is also known as a DPS race (damage per second, although damage per turn is more appropriate here). Some defenses might be set up in the beginning but after that everything is done to maximize damage. A well-designed game should not allow this strategy to dominate though. It needs to be risky. Typically the success of an all-out attack strategy depends on the boss pulling off somewhat favorable attack patterns and/or certain random effects triggering. That, and careful calculations. To make matters more interesting, the formula should not be the same for all encounters. This is relatively easy to achieve by varying the defensive capabilities of bosses. Another design consideration is to avoid bosses with too high HP because that is guaranteed to invalidate this strategy.
Although it is often to some degree up to chance to win with this strategy, the intriguing part is manipulating the odds to make that chance big enough that the time consumed by attempting the battle is on average clearly less than time it would take to grind for better characters. Various means should be available for the player to utilize. These can roughly be categorized into manipulating the odds of random effects and buying time to get more opportunities to trigger effects. This strategy is also very common in various challenges, especially towards end of the game where the level gap grows huge. It can also be present within longer battles. It is not rare for RPG bosses to assume stronger powers when they drop to low health. When that happens, it sometimes is more fruitful to switch into this strategy instead of trying to keep up with increased incoming damage. Likewise it may be the result of having limited recovery items.
Most of the time, all this is achieved by just design intuition. The third strategy here is perhaps a bit rarer than the others. In some ways, it is the hardest to integrate into a game - there's a real risk that it can become dominant if not kept in check. It demands that the system is complex enough. Also note that although this entry was written about turn-based or similar games, the same principles do apply to real-time games as well. They do however typically incorporate one very strong trick: a skilled player can evade most attacks. This also applies to turn-based games where attacks can be avoided by careful positioning of characters. Real-time games are also more likely to have stagger mechanics to prevent enemies from attacking during attack chains. These can often be utilized as stagger loops to prevent attacks.
In their respective order, these strategies go from the safest strategy to the riskiest. Likewise, the time spent grinding goes from highest to lowest. If the game is properly designed, the knowledge and planning required should go from lowest to highest, again in respective order. The strategies are also often attempted in this order. The first is pretty much the default because it's pretty steady. If it doesn't work, then it's time to look for tricks that can be used. If there aren't any available, then it's DPS race time. If none work, then it's time to check which strategy would involve the least amount of grinding. This is typically either 2 or 3, and I think this is as it should be. Player experience also determines how deep they are going to dig. Beginners might only try strategy 1, then immediately grind for experience if it doesn't work. In most games though, strategy 2 is often advertised enough so that even new players can pick it up.
I know this stuff is hardly news for anyone, but I've been wanting to put this in writing for some time now. So here it is.