The major league record holders for most games played together as teammates are...
...Chicago Cubs players Ron Santo and Billy Williams. This card is a great way to show the connection between these two Cubs greats.
I found this fact in the Cubs media guide. It is also mentioned in several places on-line. What I have never found, though, is the exact number of games they did play together. The closest I could come is this site, which says they played over 2,000 games together. If anyone can find the actual number, I would love to see it.
The runner-ups are Tigers Alan Trammel and Lou Whittaker. Their games together number is easy to find, 1918 games.
Santo and Williams played together for the Cubs from 1960 through 1973. What amazes me is that they played in so many games each season, for so long. For Santo, his record shows that from 1961 - 1972, the fewest games he played in a season was 154. Billy Williams record is even more impressive, with his fewest in the same span being 146 in his first full season, 1961. Williams also had a span of 1,117 consecutive games played during that span. Their iron-man abilities made it easier for them to play so many games together.
Their run as teammates ended when Santo was shipped across town to the White Sox after the 1973 season.
This is a record that may never be broken. In today's era of free agency, players just don't stay with the same team like they did 40 years ago. It isn't easy to come up with one player per team that has been with the team 10-12 years. I just don't think there would be two players together for that long any more.