Use programme for a noun meaning itinerary, TV or radio show, or a collection of work projects.
Program and Programme
Writers are often unsure whether to use program or programme. Those following US writing conventions don't need to worry about this. They can use the word program for everything. However, those following UK writing conventions are not so fortunate. They do need to make a distinction between program and programme. (This is because the English were influenced by the French word programme, but Americans weren't.)
Use Program for Anything Relating to Computers
For anything to do with a computer, use program. For example:
As in the second example above, the word program is the only one that can be used as a verb (i.e., programme is never used as a verb). For example:
Do you know how to program the alarm? () ()
(Usually, this will have something to do with computers.)
Please program the team-building exercises before the lunch. () ()
(Be aware that it's not always about computers.)
A box of crayons and a big sheet of paper provide a more expressive medium for kids than computerized paint programs. (Clifford Stoll) () ()
My virus checker keeps rejecting your programme. () ()
If You're British, Use Programme to Mean Agenda, TV Show or Collection of Projects
In the UK, programme is used to denote an itinerary, a show (typically, on the TV or radio), or a collection of work projects. For example:
It looks like an entertaining programme tonight. () ()
Family Guy is one of my favourite programmes. () ()
(Family Guy is one of my favorite programs. ())
The person who leaked the secret programme is hiding in Hong Kong. () ()
(Here, programme means a collecton of work projects.)
I'm glad the President finally found an economic development program. I'm just sad that it's only in Baghdad. (John Kerry) () ()
Programmed and Programming
In UK and US English, you should use programmed for the past tense and past participle of the verb to program, and you should use programming for the present participle and gerund. However, in the US, you can also use programed and programing, which are acceptable alternatives.
Americans, Just Use Program
Americans do not need to worry about the word programme. Just use program. The noun programme comes from the French, and only those following UK writing conventions need to make a distinction between program and programme.