There are currently over 40 short stories and novels by Larry Niven set in the future history of "Known Space," with more in the works. It would be practically impossible to read every single story in chronological order, as many of Niven's short-story collections are now out of print.
The good news is, readers can dive in almost anywhere. Niven's best-known novel, of course, is the multiple-award-winning Ringworld. It can be read and enjoyed as a stand-alone, but more often than not it has served as a lure, drawing readers into the vast reaches of Larry Niven's most storied universe. For those looking to stay a while, read on.
The broadest overview of all of Known Space is found in the collection Three Books of Known Space (Del Rey, 1996), which contains all the short stories from Tales of Known Space (now out of print) and has the short novels World of Ptavvs and A Gift From Earth thrown in free, as well. This collection spans the entire Known Space timeline, from the early days of solar-system exploration through the eras of Beowulf Shaeffer and the Ringworld. The book also spans a good portion of Larry Niven's career, from his very first published story ("The Coldest Place," 1964) to some more recent works ("Madness Has its Place," 1990). Not every story is a stand-out, but the collection is a must-have for readers looking to explore the details of Known Space.
Next, pick up the collection called Flatlander, published by Del Rey in 1995 (not to be confused with the short story "Flatlander"). It contains all five detective stories featuring Gil "the Arm" Hamilton. In Gil's era the Organ Banks dominate almost every aspect of daily life, sometimes in subtle ways.
The novel Protector also fits into this era and is still in print. It features Luke Garner (Gil Hamilton's boss) and introduces the Pak into Known Space. Reading Protector will greatly enhance your reading of the Ringworld novels later on.
These two books, along with World of Ptavvs and A Gift From Earth, paint the picture of pre-hyperspace Known Space. The Solar System has been settled and the early colonies are thriving. Contact with alien races has so far been limited, but it's clear humans aren't alone.
Following Protector it's time to leap to the collection Crashlander (Del Rey 1994), which contains all of the Beowulf Shaeffer stories (formerly printed in Neutron Star) and serves as a fine lead-in to the Ringworld stories, which come next. The era of Beowulf Shaeffer is, in Niven's words, "a time of easy tourism and interspecies trade in which the human species neither rules nor is ruled."
The Ringworld tales are the "last" Known Space stories, chronologically speaking (apart from the short story "Safe at Any Speed," which is in Three Books of Known Space). They are Ringworld (Ballantine, 1970), The Ringworld Engineers (Ballantine, 1979), The Ringworld Throne (Del Rey, 1996) and Ringworld's Children (Tor, 2004).
In your reading you may have noticed a gap between the Luke Garner era and the Boewulf Shaeffer era. That gap is filled by the Man-Kzin Wars, which Niven opened up to other authors (having no military experience of his own to draw upon). Baen Books published series of anthologies called The Man-Kzin Wars starting in 1988; the early ones are out of print but the eleventh in the series was published in 2005. While these stories aren't considered part of the Known Space "canon," they provide a rich and rewarding reading experience.
If you still have any stamina left after that, try searching out used bookstores or online auction sites for older short story collections to find any stories you may have missed. Explore the bibliography page for more information. Known Space is the richest of the many "Playgrounds of the Mind" that Larry Niven has built for his fans over the years. Stick around and explore for a while.