ResidentLeever: I disagree with extra lives if the game is well designed around them, so you are rewarded for exploration and don't lose
too much progression from losing all of them. Then they become a resource like food or healing items and can make a shorter and more intense game more exciting to me.
Also leads to an interesting dynamic when there's a reason to lose a life on purpose, like in Zelda 2 where you recover your HP and MP, but losing your last life sends you back to the start, takes away all your XP, and in the Japanese version lowers your three levels to match the lowest one (so if your levels are Attack 4, Magic, 5, and Life 2, after a game over they all become 2). Also, in some shoot-em-ups (including, for example, the Touhou series), dying gives you a new set of bombs to use.
That reminds me of one mechanic that does seem to have disappeared, but was quite common in the NES days, but could be considered obsolete: Only way to save is to game over. (Examples include Zelda 1 and 2, Metroid, and Castlevania 2. Magic of Scheherezade was also partially like this, but you could also save (or, rather, get a password) in mosques, but later chapters don't have one in the starting town.)
Another mechanic of that sort that has disappeared and could be considered obsolete is password saves. In some older NES and GB (and some SNES) games, when you go to save, you are given a password, and to reload, you have to enter that password. For some games, like the Japanese version of Dragon Quest 2, these passwords can get pretty long, which makes it rather annoying to save your game. (Note that this type of save system is found on the SMS (Wonder Boy 3: The Dragon's Trap; the modern remake even includes such "retro passwords", but they're not required to save/load) and probably on the Sega Genesis.)