Here's a chart from 614 analytics that displays college football national championships grouped by conference over the last century and a half. Look at all those Ivy titles!
The chart includes defunct conferences like the Southwest and classifies conferences by their current format. For example, titles won by Oklahoma in the "Big 8" are listed under "Big 12" since they're basically the same conference with a slight name change. For years when the AP and coaches split their votes the chart includes two teams (like 1997 when Nebraska and Michigan both claimed national titles).
The Big Ten and the Ivy League accounted for a lot of championships in college football's early days. However, the leather-helmet days featured fewer schools that prioritized football, which hardly resembles today's game.
The SEC has been dominant since 1950, but the conference went through a title drought in the '80s. The Big Ten's lack of titles dates prior to the current 12-year slump as the conference has only two titles since 1970 (Michigan 1997; Ohio State 2002).
From the ACC's inception in 1953 to Florida State's inclusion in 1991, the conference only won three titles (Maryland 1953; Clemson 1981; Georgia Tech 1990). Since then, the Seminoles alone doubled their titles winning in 1993, 1999, and 2013.
Check out a high-res version of the chart at 614 analytics.