Look and say sequence
Golfscript, 44 43 40 41 38 37 36 chars

Since the criterion now requires golfing, here's the golfed version:

!:^;n).+{[^\{^$^$={;\)}^if\}*].n@}*;


The original, ungolfed, version actually dealt with strings rather than abusing Golfscript's formatting conventions for dumping the stack to stdout at program termination:

# Assumes nothing passed to stdin, so input length is zero
,):$''+
{
    .puts
    # Convert to an array of [count char count char ...]
    [$\{.@.@={;\)\}{\$\}if}*]
    # Convert to an array of [[count char] [count char] ...]
    $)/
    # Form the next string
    ''\{(@\+\+}/
}
# Nineteen times. There are a *lot* of ways of generating the number nineteen
# but I like this one
$).?.)*(*