Which National League player had the most World Series rings?

Different Teams

Babe Ruth (1895-1948) holds the lead with 7 World Series (3 with the Boston Red Sox and 4 with the New York Yankees).
In the modern era, MVP runner-up Lonnie Smith had three World Series rings on three different teams during the 1980's : the 1980 Phillies, the 1982 Cardinals, and the 1985 Royals.

Total Rings
Yogi Berra has 10, and that is the most of all players in MLB history. They all came with the Yankees. From 1947, 1949, 1950, 1951, 1952, 1953, 1956, 1958, 1961, and 1962.
Frank Crosetti (1910-2002) had the most World Series wins : 8 as a player and 9 as a coach with the Yankees.