This is probably a question best suited for /r/anthropology or something similar; some of the oldest known ritualized burials are probably older than modern humans.

That's a link to a recent study of the La Chapelle-aux-Saints site where the remains of four Neanderthals appear to have been buried in depressions in the bedrock made by or enlarged by other Neanderthals camping in the area. The depressions are called "bouffias," and sometimes referred to as "burial pits."

(LiveScience has some photos of the bouffias from the 2013 study of the site.)

The skeleton we know the most about, LCS1 ("La Chapelle-aux-Saints 1") is also known as "The Old Man" because he was missing teeth and appears to have suffered arthritis for a while before his death... meaning that someone was probably taking care of him in his old age. He died around 50,000 years ago, maybe 5 or 6,000 more.

He also seems to have been buried with some bones of a cow (or aurochs), arranged like grave offerings. Or, he might just have crawled into a niche in the rock with a couple of beef bones to suck on as he died. Maybe.

(As a note, if you're into this stuff, LCS1 is also the reason why for decades people thought of Neanderthals as slouched-over, slack-jawed thugs. His body was one of the first Neanderthal remains studied, and the initial reconstruction by Marcellin Boule was done not realizing osteoarthritis had done a number on his posture.)

The pre-Anatomically Modern Human origins of burials is still slightly controversial, but the preponderance of evidence seems to be on the Neanderthals-did-it side. The main text people cite when talking about this lately is Paul B. Pettitt's The Palaeolithic Origins Of Human Burial, though I admit I haven't read it.