I did just that. It's called a 401(k). I've been averaging double digit returns over the past 30 years. Now I have enough saved to not worry about what I'm going to get from Social Security.
Though I do wish I didn't have to pay all that FICA money out over the years! I would have gladly given up my rights to benefits in exchange for getting out of the FICA program entirely.
Wow, that's pretty incredible giving an 8% average annual return is what is assumed.
All three of my teenaged kids work part-time jobs. Two have access to 401k plans which are rockin' the house. If they keep this up over their 30-40 working lives they should be set. If only I had started a 401k when I was in my teens (sigh).