Three consecutive pennants 1903-2020. Four. FIVE!

Yankees manager Casey Stengel
front cover Baseball Digest, October 1953

At least three consecutive pennants (World Series win BOLD) has been done 16 times, 8 by the Yankees, the only team with a streak greater than 3: 5 twice, 4 twice.

At least three consecutive World Series championships:
5: Yankees: 1949-1953
4: Yankees: 1936-1939
3: Yankees: 1998-2000
3: Athletics: 1972-1974

		1	2	3	4	5	Pen	WS	WS con			Managers
Chicago	Cubs	1906	1907	1908			3	2	2	Cubs	1	Frank Chance
Detroit	Tigers	1907	1908	1909			3	0	0	Tigers	2	Hughie Jennings
New York	Giants	1911	1912	1913			3	0	0	Giants	3	John McGraw
Philadelphia	Athletics	1913	1914	1915			3	0	0	Athletics	4	Connie Mack
New York	Giants	1921	1922	1923			3	2	2	Giants	5	John McGraw
New York	Yankees	1921	1922	1923			3	1	1	Yankees	6	Miller Huggins
New York	Yankees	1926	1927	1928			3	2	2	Yankees	7	Miller Huggins
Philadelphia	Athletics	1929	1930	1931			3	2	2	Athletics	8	Connie Mack
New York	Yankees	1936	1937	1938	1939		4	4	4	Yankees	9	Joe McCarthy
New York	Yankees	1949	1950	1951	1952	1953	5	5	5	Yankees	10	Casey Stengel
New York	Yankees	1955	1956	1957	1958		4	2	1	Yankees	11	Casey Stengel
New York	Yankees	1960	1961	1962	1963	1964	5	2	2	Yankees	12	Casey Stengel	Ralph Houk 3	Yogi Berra
Oakland	Athletics	1972	1973	1974			3	3	3	Athletics	13	Dick Williams	Dick Williams	Alvin Dark
New York	Yankees	1976	1977	1978			3	2	2	Yankees	14	Billy Martin	Billy Martin	Bob Lemon
Oakland	Athletics	1988	1989	1990			3	1	1	Athletics	15	Tony LaRussa
New York	Yankees	1998	1999	2000	2001		4	3	3	Yankees	16	Joe Torre
		1	2	3	4	5	Pen	WS	WS con
Yankees	8			4	2	2	30	21
Athletics	4			4			12	6
Giants	2			2			6	2
Cubs	1			1			3	2
Tigers	1			1			3	0
	16			12