Here's a sleek one:

 echo -n $PATH | awk -v RS=: -v ORS=: '!arr[$0]++'

Longer (to see how it works):

 echo -n $PATH | awk -v RS=: -v ORS=: '{ if (!arr[$0]++) { print $0 } }'

Ok, since you're new to linux, here is how to actually set PATH without a trailing ":"

 PATH=`echo -n $PATH | awk -v RS=: '{ if (!arr[$0]++) {printf("%s%s",!ln++?"":":",$0)}}'`

btw make sure to NOT have directories containing ":" in your PATH, otherwise it is gonna be screwed.

some credit to:

 - [this blog][1]
 - [this thread][2]

 [1]: http://unstableme.blogspot.com/2008/03/remove-duplicates-without-sorting-file.html
 [2]: http://dbaspot.com/shell/365450-uniq-without-sort-guru-needed.html