Genesis were very unique (early Genesis) later Genesis was another band completely. So there aren't too many other bands that sound like them. However, some of the features that helped to define their sound was the Mellotron, jazz influenced drums and a really integrated sound between guitar and keyboards.
With this in mind, check out early Pink Floyd, pre Dark Side of the Moon, specifically, Ummagumma, Meddle and their first two albums. Also, early Yes up to Relayer. Early King Crimson up to Red. Emerson Lake and Palmer up to Brain Salad Surgery. Early Moody Blues. Other good progressive bands include, Early Roxy Music, anything by Eno, Faust, Egg, National Health, Gong (especially their Radio Gnome Invisible Trilogy), Soft Machine's first three albums, Robert Wyatt's solo albums, you might like Nick Drake's Bryter Layter album.
None of them necessarily sound like Genesis, they had a certain theatrical quality that was uniquely theirs, but they would all sound good in the same playlist...