Linguist Merritt Ruhlen declares there are worldwide cognates for a small set of words. This drives most other linguists crazy. Even if it could be granted, they argue, that there were one original language from which all others descend, the time-depth is too great to have any confidence in word similarity. Language changes too quickly, they say, especially languages which are not written down. As writing only goes back 5-6,000 years, and an original language would have to be at least ten times as old, all similarities must be regarded as mere coincidence.
Ruhlen's counterargument is that a small set of words change much more slowly, slowly enough that we can still hear echoes. Other linguists would agree that some basic words change more slowly, but nothing like slowly enough to be useful.
With that as introduction, this is Ruhlen's list of words that he believes have been stable enough that we can find cognates in every language superfamily in the world (though not in every human language). Words in italics are cognates from supposedly unrelated languages. I took liberties with the orthography.
Who? !ku, k(w), kwi, kwi, okoe, kune
What? ma, ma, ma, mi, ma, manu, mina, minha, mana
Two ball, bala, bwar, pala, boula, bula, p'al
Water k"a, nki, engi, akwa, rtsq'a, akwa, oKwa, namaw, okho, akwa
One/finger tok, dike, tak, tik, tok, dik, diki
Arm kani, kono, gana, kang, kone, kan, Xeen, akan, kano
Bend/knee bonggo, bunqe, buka, buku, buku, bungku, buka
Hair sum, somm, toma, tsham, syam, summe
Vagina/vulva buti, butu, put, put, poccu, p'ut'e, put'i, betik, puda, butie
Smell/nose c'u, cona, suna, sun, cuntu, sna, sung, ijung, sunna, cuna
Seize/squeeze kangkam, kama, km, kama, kamu, kem, nggam
Fly (v.) par, pere, pyarr, p'er, para, para, p'hur, apir, paru
Ruhlen would also add Mama and Dada, the words for mom and dad in many languages. Traditionally, this commonality is attributed to the fact that these sounds are the easiest for an infant to say. Kaka, however, is a common word worldwide for uncle, grandfather, older male relative, and the k- sound does not come early for children.
Looking at the list, it's hard not to see it as a slam-dunk case for Dr. Ruhlen. Perhaps so. But with 6,000 languages it could just be that you could find something similar from at least one language in every family for whatever word you wanted.