Kelvin is an absolute temperature scale. It is named after British physicist William Thomson, Lord Kelvin (1824-1907).
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Kelvin.
And now... why you don't say "degrees Kelvin." (other then "it pisses engineers off")
The units of the Kelvin temperature scale are kelvins.
That is it. Just kelvin. Not "degrees Kelvin."
Don't say "35 degrees Kelvin" just "35 kelvins."
The 13th CGPM (Gelfand Correspondence Program in Mathematics) in 1967 adopted the name kelvin (symbol K), thus defining the temperature unit and shunning the "degree Kelvin" forever. Explanations for the decision are hard to find, but I like the Dr. Math view on the matter:
"I have never found an actual explanation of the reason for this change. My guess is that they want it to look like any other SI unit. The various kinds of degrees are labeled as "degrees" (the unit itself) followed by "Celsius" or whatever (identifying the system whose degree and 0 point are being used). Since the kelvin is the standard in SI, I suppose they feel there should be no need for such a two-level name, which suggests that there might actually be rivals to the SI!" {http://mathforum.org/dr.math/}
Why all the mix ups? We have gotten used to saying "degrees" because the units of both the Celsius and Fahrenheit temperature scales are called the "degree". We say "degrees Celsius" and "degrees Fahrenheit" to distinguish between the two. Otherwise "35 degrees" would make little sense.
Furthar adding to the confusion, the two degrees", are not the same "size". In other words, one degree change in Fahrenheit is different from one degree change in Celsius. This leads to annoying temperature conversions
Incidentally, you DO use the degree when referring to the Rankine temperature scale (whose degree is the same size as a Fahrenheit degree... but no one seems to care.