Instant runoff voting. Ask everyone for a ranked list of preferences, then completely ignore those preferences and only look at everyone's top choice unless their top choice has been eliminated. Numerous inherent problems, notably non-monotonicity, where voting a candidate higher can cause them to lose.
The biggest practical problem with IRV: it encourages people to vote for their preferred third-party or independent candidate first followed by their lesser-of-two-evils choice (common examples using US political parties: Green>Democrat>Republican or Libertarian>Republican>Democrat), but IRV then ignores the preference for the second choice over the third, which means voting for a third-party candidate still risks "throwing your vote away" and having your greater-of-two-evils win. So, IRV not only breaks fundamental properties that any sane voting system should have, it still doesn't actually address the single biggest problem we have with voting systems, and worse yet it pretends that it does.
I'd advocate approval voting if you need a system that's simple to use with existing infrastructure and doesn't require much explanation, or Condorcet if you have no infrastructural or political concerns blocking you from choosing the best option.
The problem is that if your candidate preference is A > B >> C and you vote for A and B (and not C), you might cause B to win, even though you preferred A. The tactic for just voting for candidate A is called "bullet voting", according to [1]. An interesting analysis [2] of the 2007 French presidential election claims that Approval Voting was the voting system that was second least vulnerable to strategic voters (behind the authors' own voting system, of course :)
Which is this?