On July 13, Wisconsin Governor Scott Walker formally declared his candidacy for the Republican Party presidential nomination. That makes 17 candidates with the qualifications to be recognized by the Republican National Committee as bona fide candidates. Pollsters include all 17. For example, see this Monmouth University Poll released July 13.
In all U.S. history, the most crowded Republican presidential primary ballots were in 1996, when there were an average of 8.1 candidates on the ballot. Because half the states place candidates on the ballot automatically in presidential primaries if they are discussed in the news media (which means, in practice, if they are recognized as bona fide by the party and by pollsters), all these 17 candidates will be on the primary ballots in states with such laws. Thus, assuming few if any of the 17 drop out before ballots must be printed in December 2015 and January-March 2016, the 2016 Republican primary ballots will be the most crowded regularly-scheduled statewide elections in U.S. history.
No state has ever had as many as 17 presidential candidates on a ballot in a general election. The largest general election ballot for President was in 2012, when Colorado had 16. Colorado required no petition, just a fee of $500. Colorado has since raised the fee to $1,000.
Since 2012, no state except Arizona has made ballot access in presidential primaries more difficult. Virginia has made it easier. Arizona formerly had no requirements except that the candidate submit a declaration of candidacy and show that the candidate had at least one worker in Arizona. In 2015, Arizona added a requirement that the candidate be on the ballot in at least two other states, or else submit a petition of 500 names.
In 2012, New Hampshire had the most crowded Republican presidential primary ballot, with 30 candidates. Virginia had the least candidates, only two. The average in 2012 was 7.25 candidates and the median state had six candidates. New Hampshire almost always has the most crowded presidential primary ballots because the state requires no petition, just a fee of $1,000.