You have an infinite loop when i < 2^30.

  static int nextOne(int theInt) {
    int answer = 1;
    while (answer < theInt && 0 < answer) {
      answer <<= 1;
    }
    if (answer < 1) {
      throw new IllegalArgumentException("Sorry, " +
        theInt + " is bigger than 2 to the power of 30 (1073741824).");
    }
    return answer;
  }

Good point. (And, as your signature indicates, this is more likely to be a static utility method.)

If I were defensively programming against unanswerable input, I'd tend towards failing fast with a single early check:

 static int roundUpToPowerOfTwo(int i) {
  if(i>(1<<30)) throw new IllegalArgumentException("Answer overflows int");
  int rounded = 1;
  while(rounded<i) rounded <<= 1; 
  return rounded;
 }

If we needed to give answers for any size integer (or at least up to 2^(2^31-1)), we could use BigInteger, whose #bitLength method is useful:

  static BigInteger roundUpToPowerOfTwo(BigInteger i) {
   return BigInteger.ONE.shiftLeft(i.subtract(BigInteger.ONE).bitLength());
  }

And if we weren't being literal-minded about the original request, it might make sense to just return the exponent rather than the power-of-2 itself, and let the caller worry about overflows:

 static int ceilLog2(long val) {
  return BigInteger.valueOf(val-1).bitLength();
 }

Of course we are ignoring negative exponents, in the integer spirit of the original question.

There, is it done to death yet? :)

float precision issues make me nervous (although it's probably ok here), not to mention log() is kind of expensive compared to bit shifting

why not just something like

def fn(n): ret=1; while ret < n: ret <<= 1; return ret

(news.yc/browsers mangle whitespace; proper formatting is left as an exercise to the reader)

To format code, add a whole bunch of returns and then indent 4-5 spaces

      (5 returns and 6 spaces later
          whitespace does what I want)

I think it's supposed to be 4 and 4, but I had some issues once and since then I just pile on returns and spaces until I get bored.

I thought it's 2 and 1:

 print 'Hello world'

Yup, that's it. A blank line before the indented block, then any amount of indentation.

Reddit is 2 and 4.

You could use that approach in Java...

 public int roundUpToPowerOfTwo(int i) {
  return 1 << (int)(Math.ceil(Math.log(i)/Math.log(2)));
 }

...but the first approach that occurred to this Java coder was instead...

 public int roundUpToPowerOfTwo(int i) {
  int rounded = 1;
  while(rounded<i) rounded <<= 1; 
  return rounded;
 }