28-15-1 Tennessee leads, maybe not as bad as you might expect. State actually held a 4-1 early advantage before the series moved to Memphis, TN in the early 1920s. These two have actually played in Memphis more times than Starkville: 14-9.
The longest streak for MSU in the series is 4 (as correctly pointed out by justinrsutton in the comments: 1910, 15, 19 & 20). State also won three in a row in the late 70s and capped off with the 1986 upset of #8 UT in Knoxville. The longest streak for Tennessee is the one they are currently on - six. The last win for State was in 1994...
1994 Tennessee @ Missississippi State (via sparky39762)
Out of the last six meetings with the Vols, the only one that was close was the 1998 SEC Championship Game. As we all know, MSU had a 4th quarter lead before surrendering two quick touchdowns and losing 24-14...and Tenn. went on to win the national title in the first year of the BCS.
In the last four meetings UT has averaged a 40.3-15.5 defeat of the Bulldogs. The 1995 game wasn't any better, in fact it was worse: 52-14. A 2-4 Tennessee team beat Mississippi State 34-3 in 2008....they have our number.
There is no common occurrence for this game on the calendar. In just the last 20 years it has been played in September, October, November and December.
As lopsided as the last few meetings have been, the score is pretty even in Starkville with Tennessee holding a 5-4 edge. State has a golden opportunity to even things up in that area of this series on Saturday.
If you prefer your history in the spoken word, here is Justin and Joe talking about it on the Daily Grind...