here's something that you could try:
point the portal gun up, and fire one off into the sky...... millions or perhaps billions of light years away, a portal would form on the first solid object larger than a person that the beam encountered.
of course, you run a slight risk there, because, say, if the object encountered was a star, as soon as you opened the second portal here on earth, boom, insta-death for all.
otherwise though, interesting idea, and with some actual calculations, could be used to travel huge distances across space effortlessly. global warming wouldn't be an issue for long, if there was a second planet on the cards. the human race would put its efforts into space travel and technology instead of meaningless civil wars. governments would compete to create the best habitable environments on other worlds, and in doing so, secure building rights on alien real-estate.
failing that, of course, become the richest and most famous person who has ever lived and who will ever live by making the first viable perpetual motion machine. infinite energy for the win.
and failing THAT, i'd start using it for my everyday life. i'd think with portals. stairs? just a convenient way to accelerate myself. doors? peh. i laugh in the face of doors. traveling anywhere? stick a portal on the side of a train and go for a coffee somewhere. an hour later, boom..... you're there.
the portal gun is the most fun game-item-when-imagined-in-real-life ever ever ever.