I remember a slogan back in the old days of playing Kings Quest that went along the lines of "Save many, Save often." Today I think most of us can relate to that statement and understand the importance of saving at the right place and at the right moment. That is why most of us can appreciate those games that allow us to save anywhere at any given time.
It can be a saving grace. A proper save can "save" you minutes or hours of game play and can provide the gamer with an advantage point to calculate the situation properly. Like most gifts, however; a save anywhere feature can be abused and "cheapen" the game. A save anywhere can work like an infinite life when utilized in the right moment. I suppose what it comes down to is the game and its difficulty.
Let us observe the benefits of the "save anywhere" feature. First off, it relieves the stress of annoying and difficult gaming. Kings Quest, for example, required a lot of item retrieval and puzzle solving where most of the wrong solutions could result in your death. Without being able to save before or near any puzzle, a gamer would most likely have to traverse half the land he or she went over just to get required item and try to solve the puzzle over again. With the "save anywhere" feature, the gamer instead just picks a save slot, names the save, and reloads if he or she fails thus negating all that extra time that would have been wasted if he or she had to start back over.
Another example of the "save anywhere" feature done well is in The Elder Scrolls: Morrowind, not so much Oblivion since you had the fast travel option. Although both games weren't too difficult often in them when you were of low level you could accidentally encounter a daedric shrine or some sort of a bandit camp with difficult enemies. A couple of ice blasts and paralysis spells cast on you and you are dead. So imagine not being able to save anywhere and encountering this and having to run on foot all over again with the possibility of running into the same enemies. Doesn't sound like a whole lot of fun to me.
Not so scary when you can as many times to benefit your outcome
Strategy Games tend to allow you to abuse this privilege as well. Take a game like Civilization for example. I have my civilization going well and I have my brunt of my army stationed in the north of my territory to defend against Romans. Out of nowhere the Carthaginians invade from the south and just terrorize and capture the cities. After swearing up a storm I just simply load up one of my saves from 5 turns ago and take some of my northern army and defend my south. No penalty for defending my nation poorly except for clicking a couple of mouse buttons in order to load up my last save.
So as you can see from the examples above, being able to save anywhere can prevent a game for being overbearingly annoying or difficult but can also make even the toughest strategy and FPS games on its highest difficulties to be a cake walk with properly timed saves. How does one determine what game should get a "save anywhere" feature and what game shouldn't?
It's a difficult question in my opinion. Take out the save anywhere in Bioshock or Civilization and you may frustrate players by having to rely on "checkpoints" as back up points, thus making the gamer play through what he or she has already played through. Add a "save anywhere" to Persona 3 and Tartarus could end up being a cake walk, a land of no worries about running into groups of shadows unprepared because you can simply trial and error with not having the risk of going through all the floors over again.
So I believe it is up to the developers to implement the "save anywhere" feature well and up to us as gamers to not abuse such a system.