Does Christianity allow Christians to celebrate other holidays? A quick search on Google will come up with several Christian holidays including:


Valentine's Day
Good Friday
Thanksgiving
Christmas


However, in many multi-cultural countries, there are often holidays which are from other religions, other beliefs or even tradition itself. For example a Chinese Christian celebrating Mid-Autumn Festival. Is that allowed?

PS: Today is Mid-Autumn Festival, the 15th day of the 8th Month on the Lunar Calendar. Chinese celebrate this day by bring out laterns, eating mooncakes, and reciting poems. It's kind of a tradition to me personally, but there are beliefs and myths behind the festival.
Nature worship is considered grave matter (i.e. sinful) because of the first commandment no gods before Me. 

Barring that traditions, patriotism and culture are compatible with Christian living.  Christianity grew up out of tradition and takes its form in the various parts of the earth because of the local traditions. 

That being said, follow your conscience, intemperate celebration is a good way to forget about God.  If you are required to attend Mass or your services on a holiday, put God first and attend.  We've always worked to Christianize pagan holidays in the past, there's no reason we can't continue to do it in the 'multi-cultural' world.