Niven wrote three sequels to Ringworld, The Ringworld Engineers, which is the best of them, The Ringworld Throne and Ringworld's Children, but as usual none of them have the thrill or the sense of wonder that the original generated. There's also a bunch of related novels that Niven co-wrote with Edward M. Lerner, but unless you're a completist you can probably leave these alone.
However, some of the earlier Known Space works, such as The World of Ptaavs, Protector and the collection Neutron Star are well worth reading.
However, our Alternative Choice is the first novel Niven co-wrote with Jerry Pournelle, The Mote in God's Eye. This is one of the great stories of first contact, a big, rambling space opera full of twists and sudden discoveries that will keep you on the edge of your seat all the way through a long book. An encounter with an alien craft sends a human expedition to the sun known as the Mote, where they discover a curious race of technologically advanced aliens who, at first, seem very peaceful. Slowly, however, we discover the devastatingly violent secret that lies behind this faÃ?Â§ade.
If you love the idea of the Ringworld, you should also try Orbitsville by Bob Shaw. The Ringworld is essentially a slice taken out of a Dyson Sphere, but Orbitsville is a full Dyson Sphere. The story, which won the BSFA Award, and its two sequels, Orbitsville Departure and Orbitsville Judgement, concern the mystery of a habitable shell completely surrounding a star, and what it might mean for the humans who discover it.