Actually there are lots of different sorts of good board games. Chess, Scrabble, Puerto Rico, Falling and Cluedo are vastly different. So I guess what I really want to talk about is one sub-type. Short strategy games. If you are designing a new game, and are deciding whether to leave out or put in some particular game mechanic, what should be your criteria?
I'm going to assume the game is already reasonably playable, has a consistent flavour(background story or metaphor) and provides fun of various sorts to a variety of player temperaments.
The three questions you need to ask about the mechanic are:
What will it cost (in set up time, rule explanation time, in board complexity, in game length, in narrowing down who can enjoy the game)
What does it gain (does it increase replayability? Does it add more fun per second than other aspects of the game? does it add strategic depth? does it improve game flow or balance?)
Is it worth it compared to other possible mechanics? What do I want my players to spend their time on, what is this game actually about (speed, skill, luck, diplomacy, artistic ability) ?
Let's take an example. Player markers. Do you make each player be a different colour, or do you make each player a different race?
I've seen this done well and done badly. Many games have fancy pictures of different many legged many eyed races with strange unpronounceable names. Some have an A5 race card per player, with a bit of background history about the race, who their traditional enemies are, with marked areas on the card where you can put your cards and pieces. Some gives races weak one off abilities with no real game impact but add flavour and give . Some give races abilities that meld well with particular play-styles or strategies. (eg: that's the resource hoarder race, that's the explorer, that's the diplomat, that's the warrior, that's defensive hedgehog, that's the chaotic newbie who needs luck)
So let's think about costs and benefits.
Having strong powers means you have to explain to everyone what the choices are, which increases setup time.
Having races as opposed to just player markers increases replayability a little bit. "Hey, I've never been the Scottie Doggians before."
Having racial powers increases replayability quite a lot ("I didn't realise that the Scotty and the Hattie powers combined like that before"), because each combination of races is a new game.
Having racial powers unbalances things (the Hattians are way over powered, you just won because you got that race)
So what about balance? I think every decision a player makes in a game should be a valid choice, not something forced with an obviously best move. And ideally there should be some benefit from planning ahead (hmm, if I do this low scoring thing now, it might enable me to do that very highly scoring thing next turn, because I have some Foo and nobody else seems to be going for Foo this game).