Famous movies starring plants:

Little Shop of Horrors (1960, 1986) - Nerdish florist finds his chance for success and romance
with the help of a giant man-eating plant who demands to be fed.
Invasion of the Body Snatchers (1956, 1978) - Invasion by alien plants
Day of the Triffids (1962) -Killer plants go on the rampage after the world is bombarded by a shower of meteorites.
Killer Tomatoes (1978) - Micro-budget sci-fi spoof, where tomatoes become killers
Return of the Killer Tomatoes! (1988) - Killer Tomato sequel
Killer Tomatoes Strike Back (1990) - Another Killer Tomato sequel
Killer Tomatoes Eat France! (1991) - Hopefully the last Killer Tomato sequel
Adaptation (2002) - A screenwriter (Nicolas Cage) has been commissioned to adapt the novel "The Orchid Thief".

Plant documentaries:

The Private Life of Plants (1995) - NOVA series by David Attenborough - includes awesome time-lapse.
The Plant (1994) - part of the Eyewitness nature series seen on PBS

Movies with plant names but actually having little or nothing to do with plants:

The Grapes of Wrath (1940)
The Blue Dahlia (1946)
Miss Tulip Stays the Night (1955)
Days of Wine and Roses (1962)
The Pumpkin Eater (1964)
What's Up, Tiger Lily? (1966)
Cactus Flower (1969)
Bananas (1971)
The Bananas Boat (1974)
Herbie Goes Bananas (1980)
The Black Tulip (1988)
Shangay Lily (1989)
The War of the Roses (1989)
Steel Magnolias (1989)
Driving Miss Daisy (1989)
Fried Green Tomatoes (1991)
What's Eating Gilbert Grape (1993)
Carmen Miranda: Bananas Is My Business (1994)
Magnolia (1999)

Information about most of the movies mentioned above, along with a many others not mentioned here, can be found at the The Internet Movie Database

Some plant movies mentioned in the Jan 1974 National Lampoon "Seed" magazine parody:

Last Mango in Paris
Bang the Mum Slowly

In case anyone is looking for a challenging project, these last two have not been made yet.