In the history of major league baseball, there have been 31 winning streaks that have reached 16 games or more. 17 of these were NL teams while 14 were AL teams. 20 of these streaks have occurred since 1900. Of the 31 streaks, two of them have started in one season and finished in the following season (1937-38 Pittsburgh Pirates and 1986-87 Milwaukee Brewers).
The longest winning streak (26 games) belongs to the 1916 New York Giants, who amazingly had another 17 game win streak during that season. They finished the season 86-66-3, for a .566 winning percentage, which is considerably lower than expected when a team puts together two streaks of that length in the same season. They finished 4th in the NL that year.
Of those 31, 5 have had a tie during the streak. Of the 5 that contained a tie, only 2 would still qualify as a streak of 16 games or more, One is the Chicago White Stockings in 1880 whose 21 game streak contained a tie in the 2nd game, leaving a 20 game streak remaining. The second is the streak put together by the Boston Beaneaters in 1891, which had an 18 game winning streak that would be reduced to a 17 game winning streak since their tie occurred after their first win of the 18 game streak.
Of the streaks since 1900, 2 would not qualify because of the tie occurring within the streak, leaving 18 true winning streaks of 16+ games in MLB history.
By removing the streaks with the ties, the longest true winning streak is 22 by the 2017 Cleveland Indians who finished the season with a .630 winning percentage. During this streak, the games were split 50/50 home/away. The most impressive wins within their streak were the 3 game sweep of the Yankees (finished the season with a .562 winning percentage) on the road. Within that streak, only 1 other opponent finished above .500, and that was the initial game of the streak against Boston. 11 of the 22 games were against teams with a winning percentage in the .395-.414 range.
The longest NL win streak (without a tie) belongs to the 1935 Chicago Cubs who finished the season with a .649 winning percentage. 85.7% of their games during the 21 game win streak were at home. This streak contained 4 games at home against the Boston Braves who had a .248 winning percentage that year. The back end of their streak (final 9 games) were against the New York Giants (.595) for 4 games, Pittsburgh Pirates (.562) for 2 games, and St. Louis Cardinals (.623) for 3 games in St. Louis. They entered the streak 2.5 games back on Wednesday, September 4 in a tight race with the New York Giants (2nd Place 2.0 games back) and the St. Louis Cardinals (1st Place). They finished their streak on September 27th up 6.0 games. Their season was scheduled to end with 4 straight games in St. Louis, but rain on June 7th caused the game to be rescheduled to September 25th. The game scheduled for the 26th was rained out forcing a doubleheader on the 27th, which is the day the Cubs clinched. St. Louis entered the series 3.0 games back, and lost the first 3 games of the series resulting in the Cubs clinching the division.
Now, let's focus on this current streak. Of the 18 MLB winning streaks (not containing ties) since 1900, the Cardinals' have played the 5th fewest games at home during their streak at 31.3% (the 2002 A's and 2017 Indians both played 50% of their games at home for reference) which is the lowest number since the 1953 Yankees (.656 winning percentage) played only 16.7% of their streak's games at home. Their opponents' end of season winning percentage based on teams played and number of times playing those teams was .470. 9 of their games during the streak had opponents with a winning percentage greater than .500, while the other 9 games were against teams finishing with a winning percentage below .400. 7 of their games were on the road against the White Sox for 3 games (.578 winning percentage) and the Indians for 4 games (.597 winning percentage).
Based on current winning percentages of their opponents, the Cardinals have faced the most difficult weighted average of opponents during their 16 game winning streak. Cardinals' opponents are currently (as of EOD 9/26) sporting a weighted winning percentage of .505. The next highest is the 1951 New York Giants whose opponents finished with a .483 weighted winning percentage.
What makes this streak so impressive is the level of competition it has come against along with the number of road games played during the streak. Only 1 team has a lower winning percentage at the end of their season than the Cardinals have now, and that streak was in 1907 and those New York Giants played 82.4% of their games at home.