In Kenya, birth registration became compulsory for whites in 1904. For all birth, death and marriage certificates, you will need to contact the Department of Civil Registration in Nairobi.
If your ancestors were of British origin but were born in Kenya, the civil registration documents may possibly be available in the UK. The National Archives, Kew hold records relating to records kept by British consulates abroad and at sea. From the nineteenth century they were obliged to send the records that they recorded to the General Register Office of England and Wales. The army also kept its own registers for at home and abroad.
The National Archives also holds some records of birth, marriages and deaths in Kenya. Unfortunately, these are not complete, but what does exist is available in record class RG 36 and covers the years 1904 to 1924. The National Archives holds a microfilm index to these, which will make your search easier. The Kenyan index can be found in RG 43. You will need to visit the National Archives in person, as these records aren't available on the website. Source.
Historical records of the Kenyan Colonial Government may be stored at Oxford, of course.
Here's that article about research at the Kenya National Archives. Quite an experience.
Thanks for the link to the info about the Kenyan Archives, at least the articles are stored in vaults. I would have been highly suspicious if the building had been destroyed by fire during the recent election unrest. Sounds like a trip to hell to even navigate the archives let alone to actually find out information. I did note that some of the papers from the death of Tom Mboya may be released, which is interesting since his family has been campaigning since 2003 for a full and complete investigation of the matter. I imagine such an investigation will be put on hold now that his widow has passed away(Jan 27/09), as has one of his sons, Peter.(2004 in a motorcycle accident).