Super Saiyan 1
He reached this form immediately after Goku and Vegeta fused during their fight with Janemba, making it seem at a glance as though he had no normal form.
Super Saiyan 2
Gogeta has the ability to transform into a Super Saiyan 2 and is incredibly strong in this form. He can challenge most of the universes strongest fighters and survive.
Super Saiyan 3
Gogeta gained this form the same time Goku gained his Super Saiyan 3 form. His power in this level can destroy the entire Galaxy.
Super Saiyan 4
This form was acheived when fighting Omega Shenron. This particular state only lasted 10 - 15 minutes instead of half an hour due to the enormous power.
Super Saiyan 5
This is just a speculation, since Goku can go SSJ5 yet not Vegeta. If he could, and they fused in this state, they would be able to make Gogeta a Super Saiyan 5 and be immensely strong.
Gogeta has the ability to transform in to a Ozaru when he looks at the full moon. He can control his Ozaru better than every none Saiyan except for Vegito.
Gogeta has the ability to transform in to Golden Ozaru when he looks at the full moon. He gained the ability to evolve to quicker than other Saiyans except for Vegito.
Super Saiyan God
Gogeta gained this form the same time Goku and Vegeta gained their Super Saiyan God forms. Gogeta is really powerful in this form
Beyond Super Saiyan God
After losing his God form Gogeta gained the energy to use the God Energy in his base form.
Super Saiyan God Super Saiyan
Gogeta gained this form the same time Goku and Vegeta gained their Super Saiyan God Super Saiyan forms. Gogeta in this form can fight against Beerus on equal footing.