E.C. Tubb's Dumarest series is pretty well certainly the single greatest influence on the original Traveller from 1977. There's a quote from Loren Wiseman in the wild to the effect of "We just copied Tubb and were surprised everyone didn't know that."
Number two among literary inspirations for the original would be H. Beam Piper's Terro-Human Future books. Space Viking is especially notable, then there's The Cosmic Computer, Uller Uprising, etc.*
All are great reads (well, I can only attest to the first 12 Dumarest books out of 32, but I'm working my way through them...)
Poul Anderson's books, as mentioned, are also among the major original influences (Ensign Flandry, The Man Who Counts, etc.) as are Harry Harrison's books.
And, yes, lots of others. Even more in later version of Trav as time has given us more great SF.
Now, I had read all the literary influences cited in the original Traveler except the Dumarest books by the time I bought Traveller in '77. And I've got to say there were a lot of things in Traveller I didn't grok even after running it and playing it for 30 years. Till I read the first Dumarest book, The Winds of Gath. Now, every chance I get, I tell fellow Travellers to get and read this book, and as much other Dumarest as you can. It's a model for everything about Traveller that the other authors don't have (and a great book!)
*There is a cross-over between Piper and Pournelle. Pournelle has described it in print, but basically Piper authorized Pournelle to use his universe, hence we have Tanith, etc. in Pournelle's works.