I agree with the moms who say it depends on the child and the room. My son was about your son's age when we started letting him be in his room by himself. I would be on the same floor as him and have the baby monitor on. When downstairs, he could play in the living room alone if my hubby or I were downstairs (our downstairs is small and you can hear everything from any place). He started playing downstairs on his own around 2 1/2 or 3.
YOU need to be comfortable with him being alone, and if you aren't comfortable yet, don't do it, or work up to it. I won't let our 18-month old play alone in a room yet because she gets into lots of stuff! If you do let him play alone in a room, consider getting down on the floor at his level and look at anything he could get into. Keeping doors to other rooms closed is always a good idea, along with having gates across stairs/other problematic areas. A couple of things to consider with "babyproofed" rooms. If there is any kind of regular bed in the room, a child can fall off it or hurt themselves by bouncing on it (my son fell off our bed several times when we were right on the bed with him). Also, if there are lamps or anything else with a cord plugged in, they can pull on the cord and have the item fall on them or pull the plug out of the outlet and you then have an exposed outlet, ripe for exploration. Things like curtains or blinds can be pulled down, causing injury. This is why we waited until our son was mature enough to understand he wasn't allowed to do any of these things, or he would lose the privilege. When you are ready, it will be a wonderful/scary thing until you get used to it. Good luck!