Inspired by this answer regarding the long-term effects of The One Ring: Sméagol possessed the ring for close to 500 years, and although he clearly didn't wear it constantly, it had some terrible effects on him. He was disfigured and incredibly old; elven rope burned him, and he found lembas to be disgusting; and his personality definitely changed. He was very obviously subservient to The Ring.
But despite the linked quote ("if the Ring overcomes you, you yourself become permanently invisible"), Gollum never became a wraith. I can hardly imagine a Ring having more power over someone than it did over him. What more would it take for someone to be "overcome" by it? Or is this another example of Hobbits' strength of heart? -- As Frodo was able to resist the Ring's influence until he came to the edge of the Cracks of Doom, so likewise Sméagol was able to be almost completely corrupted by The Ring yet remain corporeal?