Yes. In academic style you'd probably avoid it. But in other styles it's fine.
Here is an example of "But" in sentence initial position from journalistic style -an article from the Easyjet in-flight magazine called
Sweet Charity.
The 36,000 runners who pounded the course at this year's london marathon have long since recovered from their blisters and aching limbs. But for Zarine Kharas, the work is far from over.
And
here's another one :
By and large the charities don't begrudge it for taking the hassle out of collecting so much cash on their behalf. But should moneymaking mix with the charity world?
In
this online article in The Guardian both "And" and "But" are used not only to start sentences, but also to begin paragraphs. If you look at it you'll find 4 examples of "But" being used initially and one of "And":
And we must stop the situation in which the government can take 30 days or more to pay producers.
"Or" is used in the same way - Here's an extract from
an article on cricket :
Are we really to believe that a first-class team can make 123 in 6.1 overs against first-class opposition? Or that Salman Butt, whose fastest innings in terms of strike-rate in the international arena is 36 from 31 balls, could make 92 from 25 balls?
However, "but" is the most common - here's
yet another article at random - it has four initial uses of "But" and none of the others.