The Columbia Lion is the university mascot, and was adopted in 1910.
The idea was originally suggested by George Brokaw Compton (CC 1909).  Interestingly, the Lion motif had been around campus from before, appearing for example on the roofs of Low Library (built in 1895) and other buildings.
The idea was first proposed at the April 5, 1910 meeting of the Alumni Association, where it was enthusiastically endorsed. The resolution by Compton (who explained 'we have the King's Crown, let us have the Lion,') was accompanied by the presentation of a blue and white banner emblazoned with a lion rampant and the motto "Leo Columbiae" by the Society of the Early Eighties.
As might be expected at Columbia, the resolution was the focus of some controversy, carried mostly in the form of a furious month-long exchange of letters and editorials published in the Spectator and alumni publications. Some argued that the lion was too royalist and that the eagle was a more appropriate symbol. Others lobbied for the adoption of Matilda the Harlem Goat as the school mascot. The Spectator, of course, also weighed in with its opposition to the Lion, coming down on the wrong side of history. But by May 4, the Student Board had approved the lion mascot.
However, the mascot initially proved to be a dud. This may have been a result of the school's ban on football. Anyway, with the opening of Baker Field, the Class of 1899 decided to grace the field with a bronze lion for its 25th anniversary year. The Lion was sculpted by Frederick G. R. Roth, and placed on a plinth with three quotes from scripture. The Lion was originally located atop a rocky ledge overlooking the football practice field from the east side of the complex. In 1962, the sculpture and plinth were moved 80 yards to just outside Christie Field House to make way for the baseball and soccer fields.
In 1928, the Columbia mascot took on a more visible position as the logo for Goldwyn Pictures Corporation, and subsequently MGM after the studio's merger. MGM's lion, "Leo", was the creation of Howard Dietz (CC 1917, J '?), who created it for Goldwyn Pictures while working for the Philip Goodman Advertising Agency. It is said that he was inspired by Columbia's fight song, "Roar, Lion, Roar".
Other appearances of the lion around campus include "The Scholar's Lion," a sculpture by Greg Wyatt CC 1971 outside Havemeyer facing the Business School which was gifted to the university in 2004, the "Teaching Lion" by Stanley Wyatt CC '43 in the Rosencrans Reading Room on the ground floor of Butler Library, and the bronze Lions head sculptures at the end of Butler Plaza flanking the steps in front of the Library among other places.
The Lion Mascot
On October 15, 2005 Columbia debuted its revamped college mascot, Roar-ee. The name "Roar-ee" was selected in an internet vote, beating out four other finalists: Hamilton, Hudson, K.C. and J.J.. The athletics department received over 200 submissions in the initial round of its "Name the Mascot" contest that had begun in September.
Roar-ee's unnamed predecessor who bears a suspicious resemblance to Disney's character The Beast.
The Lion Logo
Like any school logo, the Columbia's lion logo has had many forms.
The most recent form of the logo was first adopted in 1999. Then-AD John Reeves wanted to replace a collection of between six and ten different logos, including the Detroit Lions logo, and a series of designs that had earned the derogatory nicknames "lettucehead" and "cabbage-head." The logo featured a front profile of a lion with paw extended, and appeared either with or without the New York City skyline in the background. According to Reeves, he was looking for a new logo that "kinda had a kind face, but [was] also capable of attacking, because we want teams to think of us as a kind, sportsmanlike people but not to take us for granted." The logo was created by Kim White, Emily Johnson, and Junie Lee under the guidance of art director Sandy Kaufman of public affairs. The logo cost $2,000 to create, but Reeves considered it a bargain, noting that other ivy league schools had spent between $40,000 and $60,000 to do the same. As part of the logo design process, the department had to settle on a definition of Columbia Blue, choosing Pantone 292. The logo redesign was accompanied by the introduction of a new lion mascot costume on February 12, 2000, thanks to the generosity of Robert Berne CC '60 B '62, who had been the mascot in his time as a student.
In 2005, as part of a re-branding effort by new AD M. Diane Murphy that also included the introduction of Roar-ee, the logo's colors were lightened, and the skyline and lion's tail were dropped. The following year the entire body was scrapped, leaving only the lion's roaring head under the school's name. However, the bookstore uses all iterations of the logo indiscriminately on merchandise and apparel (as it also does with the Columbia Crown).
An AIM Buddy Icon claiming to be a Columbia logo ca. 1930
An old athletics graphic
Another old athletics graphic
"Lettucehead" (I think.) 
The Detroit Lions based logo 
The Scholar's Lion
Other manifestations of the lion
- "Leo Columbia", Columbia Alumni News, 6 April 1910, Vol. 1 No. 28. Additionally, an 8x10 black and white photograph of this banner can be found in the "Columbia Lion" Subject File in the University Archives.
- Roth's Columbia Lion at Baker Athletic Complex
- Columbia Unleashes New Lion, Columbia College Today, February 2000
- The Lion Enters Slick New Era, Columbia Spectator, Nov. 11, 1999
- Within 10 years, the University would determine that Pantone 290 was the color instead. It's unclear if they changed their mind or simply didnt know what had been done 10 years previously.
- Taken from Sportslogos.net