Hitting for the cycle is a relatively rare feat. To accomplish a cycle, a player must get a single, double, triple, and home run in the same game. A four-hit game is rare enough, but to include each of the four hits is a significant feat. In fact, it is on par with a no-hitter in rarity.
A "natural cycle" is hitting a single, double, triple and home run in order in a game. Obviously, it is even rarer.
The term itself was first used in 1921, but did not became popular until the mid-1930s, a high-hitting era that saw more cycles hits than during any other period in major league history.
The first player to hit for the cycle was George Hall, playing for the Philadelphia Athletics on June 14, 1876. There is some question about his feat, however, as some accounts of that game list him with three triples, a single and a homer, and others with two triples and one of the other three hits.
Four players have hit three cycles in their career: Long John Reilly, Bob Meusel, Babe Herman and Adrian Beltre. Beltre was the latest to join in 2015 when he hit his third. 31 players have hit for the cycle twice. In 2012, Aaron Hill hit two cycles in a span of 11 days, joining Herman who had hit two cycles in 1931 (but over two months apart) and two 19th century players, Reilly and Tip O'Neill, who had done so in 1883 and 1887, respectively. In 2018, Christian Yelich joined the group by hitting two cycles against the same team, the Cincinnati Reds, less than a month apart. In Game 3 of the 2018 American League Division Series, Brock Holt of the Boston Red Sox became the first MLB player to hit for the cycle in the postseason. Three players have hit for the cycle in both leagues: Bob Watson, John Olerud and Michael Cuddyer.
Researcher Herm Krabbenhoft has argued that while the cycle is a remarkable feat, what he calls a "quasi-cycle" is even more impressive. To achieve this, a batter must accumulate the three extra-base hits and add a fourth extra-base hit (be it a double, triple or homer). Such games are even rarer than a cycle (there were 88 from 1876-2016, as opposed to 313 cycles), but are then largely forgotten because they don't fall into a neat category.
This can lead to a dilemma for a player who needs just a single to complete the cycle, but hits a ball that would normally result in a double or triple; does the player stop at first and add his name to the prestigious list, or continue to the next base, ensuring his game is likely to be forgotten. Krabbenhoft also studied that conundrum, and could only find very few cases of a player deliberately stopping at first base to ensure a cycle, the most obvious being Jeff Frye, playing for the Toronto Blue Jays on August 17, 2001. His "single" in the 7th inning scored a baserunner all the way from first base, and he explained after the game that he had been told by his coach and manager to stop at first base. It helped that the Jays had an insurmountable lead at the the time.
- David Adler: “These are the coolest cycles ever”, ‘’mlb.com’‘, June 19, 2020. 
- Michael Huber and Allison Davidson: "Origin of the Phrase 'Hitting for the Cycle' and an Approach to how Cycles Occur", Baseball Research Journal, SABR, Vol. 47, Nr. 1 (spring 2018), pp. 112-119.
- Matt Kelly, Do-Hyoung Park and Andrew Simon: "These players hit for multiple cycles in their careers", mlb.com, April 25, 2020. 
- Herm Krabbenhoft: "Quasi-Cycles - Better than Cycles?", Baseball Research Journal, SABR, Volume 46, Number 2 (Fall 2017), pp. 107-111.
- Herm Krabbenhoft: "'When You Come to a Fork in the Road, Take It'; Who Took the Cycle or Quasi-Cycle?", Baseball Research Journal, SABR, Vol. 47, Nr. 1 (spring 2018), pp. 72-80.