Below I present a U.S.-focused list of electoral reforms roughly in order of the importance that I place on them. Others will certainly have strong disagreements, and I'd love to hear from you. I'll update this post over time with additional explanations for the other electoral reforms.
Top-two primary
The 2016 election for U.S. President is a shining example of the problems with conventional primaries (likely producing the most disliked major-party candidates ever). Although voters are increasingly identifying themselves as independents rather than being affiliated with a political party, the Democratic and Republican parties hold enormous control over the electoral process.
For most elections, the Democratic part has a primary to elect its candidate, the Republican party has a primary to elect its candidate, and later an election is held to decide between the Democrat and the Republican (and sometimes third party or independent candidates).
Conventional primaries produce bad election outcomes because (i) they elect partisan candidates rather than moderate candidates, (ii) the parties have too much control (e.g., "super" delegates), and (iii) third-party or independent candidates are essentially shut out of the electoral process.
Instead, a primary election should be open to all candidates who have qualified for the ballot. A candidate may identify a political party that they identify with, but the political parties would not have any significant involvement. The top-two winners (who may identify with the same party) then compete in a run-off election to determine the winner.
Even better, the winner could be determined in a single election using instant runoff voting and there would be no primary at all!
A top-two primary should allow for more moderate candidates rather than partisan candidates, give more power to voters rather than political parties, and elect candidates who better represent the will of the voters. Reduced partisanship should hopefully help with the other electoral reforms described below.