Poison counters are an old mechanic - creaky, even - but notable as the first alternate win condition mechanic other than milling. Everyone knows how poison departed Magic for a long time, had Mark Rosewater backing it for block after block (even having tried to base the fabled "Bogavhati" block that became Tempest block around poison entirely) before betting it back in Scars of Mirrodin. Still, despite all that, for all the counters permanents can get on them, players can so far only have poison counters. But that could easily change, according to Mark Rosewater on his Tumblr blog.
When deetsposts asked, "Has there been any discussion on giving players counters that aren't infect? It seems like there's a lot of design space there," Rosewater replied,
You’d be surprised how close we’ve come in the past to other counters. I’m sure we’ll do it some day.
In the comments, voicesofchaos correctly points out "Eldrazi Spawn were almost mana counters players had," and gold counters are a stereotypical enough custom card mechanic that it's possible that Theros block's gold tokens were originally player counters. Besides that, the most often designed kind of player counter is an inverse poison counter that gives you a game win for accumulating enough. Sometimes these ("elixir counters") cancel out like +1/+1 and -1/-1 counters, a fact which has been designed around. Either way, the size of the design space is much bigger even than that; there are a whole host of ways counters on players could be used to represent accumulating both positive and negative long-term effects.