Though not deliberately shiny locked, Mew had a fixed set of IVs in Generation II, that did not meet the shiny requirements.
Though not legendary, it was an event Pokemon. It should be noted it's the only normal Pokemon that has an unobtainable shiny form.
Reshiram & Zekrom
These are the only in-game legendaries that are confirmed to be shiny locked.
Victini, Keldeo & Meloetta
As with almost all event distributions, an event distribution Celebi cannot be Shiny. [...] While it has been shown that the Celebi sent to the Colosseum save file can never be Shiny, there is no conclusive evidence about the potential for the Celebi sent directly to the GBA to be Shiny.
Xerneas, Yveltal and Zygarde (unconfirmed)
Although a very high chance, the fact still stands that there is currently no hardcore evidence that they are shiny locked (except for the fact that no one on the internet has found a shiny Pokemon). People are doubting Zygarde is shiny locked, however, as Kyurem, the 'third legendary' of Gen V was never shiny locked.
Hope I helped. :)