Yep I agree with Griff - long tones, practice, determination and dedication, and remember that quality of practice is is more important than quantity of practice with regards to developing a sound - lots of listening to styles of playing you like will help.
I think I differ from most. I don't read music and I didn't have a teacher. I didn't spend months choosing mouthpieces or saxes for that matter. I bought a sax from the devils junk yard, I had it serviced, I bought a mouthpiece that I liked the look of, again from ebay and I played along with cds that had sax players that I liked. Players like "Blue" Lou Marini from The Blues brothers, Wes Magoogan from Hazel O'Connors Will you? Not to forget Clarence "The big man" Clemons from Bruce Springsteen's E Street Band.
There were others, too many to mention them all. I then started to get a sound that I liked. In fact, I think my sound is very versatile. I can play soft smooth ballads with the sax sounding almost French horn like, or I can play raunchy Rock 'n' roll. All using the same set up. I didn't do the scales (I wish I had, don't get me wrong, I'd be a lot better than I am and I'd have got there a lot quicker too) I didn't do the long tones, although I do now, I just played for hours, playing along to the same track over and over again until I thought it sounded ok.
Then I went out busking and it all started to come together. Now I need to learn my scales so that I can speed up my fingers and learn some more technical tricks and licks! (And stop being so plody and predictable)
You own sound is the same as your own voice. Others may speak with the same tones, accent, and vocabulary, but most of us have a recognizable voice. When you have taken care of the basics and can play what you hear, then it's not much different to singing. The way you phrase, and think about melody will make this your own. It should be obvious that if you are trying to sound like someone else, that's not really your voice. Too many get hung up about finding a favorite player who they try to imitate. I guess that's OK, but it's certainly not giving yourself chance at having your own sound.
Play a lot- nick sounds, runs, techniques from other players (and CDs, other instruments etc)- keep the bits you like, discard the rest- sooner or later it ends up sounding unique due to the eclectic mixed bag of stuff you’ve absorbed….. simple, or as complicated, as that! As came up on another thread- at times I owe as much to Irish Pipes and Jimi Hendrix as I do other sax players.....