Is it possible for a private citizen to have a 900 number as their personal home phone number?
I don’t see why not. You’d just have to convince enough people that talking to you is worth $1.95 a minute. 
A quick google on “900-number provider” yielded a sponsored ad from PayPerCall.com, who quote a setup fee of 800 dollars, a per-month cost of 50 dollars, and a choice of costs per call. Dunno how rigorous their customer qualification is…
I know plenty of people who should pay me $1.95 a minute to listen to them babble.
Certainly.
To have either 800 or 900 service you need to have an conventional local number for the call to be sent to.
900 service is much like 800 service. It’s simply an add-on where calls to that 800/900 number are forwarded to your actual local number. The entity doing the forwarding tracks the call detail info (from, to, start time, duration) and sends a billing record for the appropriate $ to the appropriate local provider & account#.
For 800, they bill the number forwarded to, and for 900 they bill the caller.
bottom line: You don’t get a 900 number instead of your current number, you get it in addtion to your local number.
What the OP is probably referring to is a 500 number, aka “follow me” personal communications service.
Didn’t AT&T pull the plug on those?
Standard call forwarding to a cell phone would easily cover this. I do it every day for my business.
I don’t think they could, as it is the North American Numbering Plan, not one specific phone company, that defines such things. They’re still listed in the official plan (see www.nanpa.com).
I suppose AT&T could decide they would not participate in this, just leave the business to other companies.
It may be that technology has passed this option by. It was designed back when nearly all phones were land lines, and there were no nationwide cell phones. Like drachillix says, call forwarding to a cell phone can do this now.
(edits mine) The 500 area code may be in the NANP, but I had read that AT&T was the only provider of 500-numbers, and decided to quit the business. I could be wrong, though.
You appear to be.
The NANP site (http://www.nanpa.com/nas/public/formPCSMasterReport.do?method=displayPCSMasterReport)
lists hundreds of assigned 500- numbers, from America West to Zeke’s General Store & Internet Communications Company. But no AT&T that I could see. (Of course, wasn’t that company split up 20-some years ago?)