Keep in mind that the room size is not really your actual usable playing area. My own room is 3.6m (11.8 feet) by 8.8m (28.8 feet), but the playing area is actually a bit smaller than that because I need to be able to take a back swing, and I don't want to risk smashing my bat against the walls.
Minimum Amount of Room For Family FunA full sized table tennis table is 2.74m (9 feet) long by 1.525m (5 feet) wide, so you had better have a little more than that amount of space or you'll be sitting on the table to play! Seriously though, for a fun family game of singles ping-pong, assuming the players are relative beginners, you can probably get away with 1.5 - 2m (5 - 6.5 feet) behind each endline, and maybe 1m (3.3 feet) to each side. Maybe even a tad less if you don't mind leaning on furniture or hitting your bat against the wall every now and again.
If you are going to play a lot of family doubles, I'd recommend another meter (3.3 feet) at each endline, and 50cm (1.64 feet) on each sideline, just to give you room to get around your partner. Otherwise you'll probably have to play tennis doubles, where each player can protect his own side and hit the ball out of turn.
Minimum Amount of Room For Robot TrainingIf you are using a robot to train, things are different. You'll need less room at the robot end, since you only need just enough to squeeze the robot up against the wall. This gives you a more room on your side of the table, which is good. From there, it once again depends on your standard, not to mention your style of play. Beginners will probably need less space than advanced players, and close to the table hitters and blockers will need less room than choppers and loopers. I'd say you would be looking at an area behind the endline of at least 2m (6.5 feet) depth for beginners, and for advanced defenders and loopers 4 - 5m (13 - 16.4 feet) of depth would be preferable.
In terms of width, you can get away with a smaller area if you are willing to go to the trouble of moving the robot and table to allow you more space on the forehand or backhand. Of course, this won't help if you are doing a drill involving both sides of the table. My own home room is 3.6m (11.8 feet) wide, and this works quite well for most angles. So another 1 - 2m (1.3 - 2.6 feet) wider would be nice if you want to really work your crossover footwork, but you could get away with only about 2.5m (8.2 feet) provided you don't do any side to side drills.
Minimum Amount of Room For Multiball/Feeder TrainingWhen the feeder stands behind the endline, this is pretty similar to the robot training space requirements (perhaps a touch more), since the feeder doesn't need all that much space. When the feeder stands next to the sideline, you will actually have even more space available for the trainee in terms of distance from the endline, because you can push the table just about right up against the wall (although I'd recommend hanging a loose blanket or plastic garbage bag a little in front of the wall to stop the balls bouncing back onto the table, which is distracting. The netting from a robot would be ideal too). You also need a little room on the sideline the feeder is standing on for him to be able to swing his racket when feeding balls.
Minimum Amount of Room For Intermediate to Advanced PlayersThis is quite a tough call to make. It really depends on the styles of you and your training partners or opponents. And bear in mind that a solidly enclosed room feels smaller than the same area marked out by barriers in a large training hall. The ITTF stipulates the following court size for Olympic and World Championships,
3.02.03.01 The playing space shall be rectangular and not less than 14m (46 feet) long, 7m (23 feet) wide and 5m (16.4 feet) high, but the 4 corners may be covered by surrounds of not more than 1.5m (4.9 feet) length.,
but many National level events (at least here in Australia) tend to use court sizes of 12m (39.4 feet) long by 5m (16.4 feet) wide. So if you are lucky enough to be anywhere near that size you are probably going to be in fairly good shape. If your area is much smaller than 10m (32.8 feet) by 4m (13.1 feet) you are probably going to be bouncing off the walls a lot, and you should probably consider doing more multiball training to simulate match conditions.