"far-reaching influences" is correct and usable in written English.
You can use it to describe the wide range of effects that a decision, action, or event has had. For example, you could say: "The decision had far-reaching influences on the entire industry."
More than a great listen, the set solidifies both Can's oeuvre and their approach to music making as far-reaching influences.
Because of their far-reaching influences, Pinkshinyultrablast's debut album - Everything Else Matters, released earlier this year – drew comparisons to Slowdive and Lush, a sound they say is unlike the rest of the "stagnant" indie scene of their hometown.
In the hopes of gaining a deeper understanding of these remote areas and their far-reaching influences, the worldwide research community is preparing for International Polar Year (IPY) in 2007.
Metabolic modelling may further yield far-reaching influences on practical applications as well, and serves as a bridge between molecular/biochemical research studies and the optimisation of wastewater treatment plant operation.
As sexual coercion and its adverse health consequences may bring about far-reaching influences in one's life, intervention efforts to promote youth development and discourage health-risk behaviors should be supported, with particular consideration of gender disparity.
Our findings demonstrate the far-reaching influences of biomedical approaches to CLBP including the powerful influence that healthcare practitioner beliefs and communication can have on a person with pain.
He showed himself a mordant editorialist with far-reaching influence.
The Swedish Academy had selected Sartre for having "exerted a far-reaching influence on our age".
Whatever the compiler did decide to include had a far-reaching influence.
During finance's most powerful period, the industry exercised far-reaching influence on governments and regulators.
In 1838 and 1839 Newman was beginning to exercise far-reaching influence in the Church of England.
