Colbert is one of the best comediennes of her era (the 1930s and 40s) as well as one of the most stylish stars of the movies.
Her career started in the 1920s, when she was just a girl. She was born in France--actually, in the eastern Parisian suburb I lived in on sabbatical--in 1908, so her first movies, made in 1927, were when she was just 19.
Like Davis, she made a bunch of minor melodramas initially, really breaking out in 1934 with It Happened One Night, with her co-star Clark Gable. For both of them, it was a break-out picture, but before she made this, she made 26 films between 1927 and 1934. Any of those are fun, but it was her appearance as the Empress Poppaea with her bath of asses' milk that made early censorship happen. Forget Janet Jackson--this is the original peek-a-boo, and Colbert is great, just acting while naked. But don't ignore the "slavegirls'" BDSM chains and peek-a-boo dresses, either.
Her final, great film might be The Egg and I (1947) with Fred MacMurray (of future My Three Sons' fame). Like Davis, in the 1950s her career turned to TV, but by 1961 she was done, retired from the spotlight, until her final appearance in 1987. Unlike most actresses, she had only two marriages, one short when young, and one long marriage to a surgeon who died in 1968.
My favorite Colbert films include:
The Wiser Sex (1932) with Melvyn Douglas and Franchot Tone, two very classy actors no one knows anymore.
I Cover the Waterfront (1933)
It Happened One Night (1934), the great classic comedy
Cleopatra (1934) -- watch this, then the Liz-and-Dick one. Laugh!
Imitation of Life (1934) which also stars the great Hattie McDaniel; later this was a Lana Turner tear-jerker of the 1950s, of the same title, with the great Juanita Moore. I prefer the Colbert version, perhaps because it is more honest about the issues of "passing" and race that are central to this piece.
The Gilded Lily (1935) with Fred MacMurray and Ray Milland.
I Met Him in Paris (1937) with Melvyn Douglas and Robert Young, later of Father Knows Best on TV.
Bluebeard's Eighth Wife (1938) -- a pretty great comedy with Gary Cooper.
My personal favorite of all is The Palm Beach Story (1942), with Joel McCrae, Rudy Vallee, and Mary Astor. Simply brillant! Here's the trailer, with French subtitles.
Since You Went Away (1944) is one the host of "at home" picture studios made during WWII about life without husbands and fathers. It also stars the beautiful Jennifer Jones and Joseph Cotton, who were a great movie couple as well.
The Egg and I (1947) is charming and surprisingly holds up well. It includes Ma and Pa Kettle, too, so if you've never seen Marjorie Main in this role, definitely find it!
Colbert's films are definitely a record of the star system (she refused to be filmed from the left, for instance, after learning about film lighting) and the studio/contract era of Golden Hollywood. Unlike davis she was never considered a "great" actress, but watching her films you see that she had strong comic timing, the ability to handle complex language (whether comedy or drama) as well as weaker dialogue (and make it look good), and that she was a professional. She, too, made the transition from ingenue to "mature" roles gracefully.