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There are many languages without the /w/ sound as in English world, as in French oiseau, as in Spanish fuego, and as in Mandarin wang (the last three respectively mean bird, fire, and king). Some famous examples include: Russian, Yiddish, Albanian, Armenian, Greek, and Turkish.
But, languages without the /j/ sound as in English yellow, and French caillou (which means pebble) seem to be extremely rare.
So, why is the /j/ sound so common in human languages?
Some examples drawn from Phoible are Ket, Khasi, Garo, Malay (Standard), Iai, Kaliai, Maori, Hawaiian, Asmat, Kunimaipa, Nasioi, Kalaallisut, Eastern Ojibwa, Ticuna, Ocaina, Guarani, Liberian Kpelle and Khoekhoe. However, one should also dig into the original data sources. A non-original data source, Wikipedia, cites [qàj] 'elk' in Ket; the unglossed root <layang> = [lajaŋ] is given in the Wiki page on Malay phonology. Wiki includes [j] in the inventory for Kalaallisut, but Phoible also lists [j] as an allophone of the phoneme /ʝ/ (dunno why the phoneme is deemed to be /ʝ/ and not /j/). It also lists [j] as an allophone of /ɲ/ in Liberian Kpelle, but also drawing on a different source, it is a full-fledged phoneme. Having worked on the Guinean dialect, I would agree that /j/ is a phoneme of Kpelle, and certain exists as a sound of the language. In other words, some of the gaps are artifacts of analysis. The one case that I am mostly convinced of is Khoekhoe, having worked on the language: it has no [j] at any level, though Hagman in his grammar suggests that [j] exists in loanwords (no examples are given).
A bizarre "example" is Finnish, which according to one Phoible source (Stanford Phonology Archive) has no j (!!!?), because the phoneme is actually /e̯/ and [j] is merely an allophone. There's really no doubt that Finnish has /j/ (jarvi, jalka, joki).
In Russian, the consonants are arranged into 4-member squads: hard voiceless, hard voiced, soft voiceless, soft voiced. The [й'] sound is voiced counterpart of [х'], and voiced soft counterpart of [х]. Thus, this squad is lacking only voiced hard member. This sound, by the way, can be found in Ukrainian.
So, I think, having voiceless velar fricative [х] in your language or its allophones (such as uvular fricative) strongly prompt you to have its contrasting soft, voiced and soft voiced squadmates.
