Do citizens of the Federation have private starships?

[Zed Snardbody]

I think the problem that we encounter is the association of humans with the federation. Humans don't use money, the federation might. We here credits mentioned on occasion, perhaps the federation does have a currency, just weak one. You can make money in the federation, but your better off working your ass off and getting the hell out of there and making some good gold pressed latnum so your dollar/strip actually has some weight to it.

[Shrykull]

In SW we see that it's relatively easy if you have the money to have your own private ship. Have any of you ever seen people in the Federation own or have their own private ship?

Yes. Okana ran his own ship. From the TNG episode "The Outrageous Okana"

He wasn't from the federation.

[Stravo]

Okuna was from another alien race. Harry Mudd comes form the TOS era, and the current train of thought is that a change took place between TOS and TNG era that shifted to a more communistic form of government. In the same episode with Harry we have a mining settlement privately owned. The same in Devil in the Dark, a private corporation runs the mines with the Federation providing security to the company.

Yet most instances of privately run mining companies lie outside the Federation in TNG era (Ezri's families' mines lie outside Federation influence.)
Any instances of private ownership must be looked at in TNG era because it was fairly obvious that in TOS era there was a healthy enightened capitalism going on.

[Natorgator]

What about "Little Green Men" when Quark got his own ship?

[Shrykull]

What about "Little Green Men" when Quark got his own ship?

DS9 is in the bajoran system and Ferginar isn't part of the federation either.