Lowest-Base Palindrome
GolfScript, 20 characters
~:x,2&gt;{x\base.-1%=}?

A different approach with GolfScript other than Dennis'. It avoids the costly explicit loop in favour of a find operator. Try online.
~:x        # interpret and save input to variable x
,2&gt;        # make a candidate list 2 ... x-1 (note x-1 is the maximum possible base)
{          # {}? find the item on which the code block yields true
  x\       # push x under the item under investigation
  base     # perform a base conversion
  .-1%     # make a copy and reverse it
  =        # compare reversed copy and original array
}?