How do you say I dream therefore I exist in Latin?

Literally, Somnio ergo sum ("I dream therefore I am").

Be aware, however, that Latin somnio, at least in Classical usage, doesn't have quite the same connotations as English "I dream". The English Word can have the quite positive figurative meaning "to imagine a better future". The Latin Word, by contrast, implies idleness or delusion. Other translations for this positive sense of "I dream" might be spero, "I hope", or perhaps meliora cogito, "I imagine better things".