The ball may hit the net but in a way that does not alter its course or prevent it from hitting either side of the table. The ball still has to be going fast enough for a player to return it, and if a player can’t return a shot there’s no point making the shot in the first place.
If your question is if the ball is allowed to go over the net, yes it’s allowed as long as your opponent can still return it.
The answer may vary between tables and tournaments if they have different rules, but in general, it’s fairly similar everywhere. It also depends a bit on what type of table tennis you’re playing since there are different types of tables.
I can’t speak for all tables and tournaments, but I’ll try to give a general answer that should be fairly accurate: The ball must not hit the net (or net posts) on its way over to your opponent. Whether it’s allowed to go above the net onto the opponent’s side is up to the opponent; if he or she chooses to let it go, then it’s allowed. If they choose not to, the ball must bounce twice on your side before you hit it over again. This is pretty much true for all of the table tennis unless stated otherwise.
I play in Canada, and I’ve never heard of anyone getting a point taken away if their ball hits the net. If this is true in your country or tournament, it’s at most an extremely minor mistake that would only be noticed by the most attentive observer.
The spirit of the game says “playful”. Hitting it over whether it hits the rim or not is part of that spirit. It’s no different than when someone returns your shot in such a way that you have to do something out of the ordinary (e.g. jump) to get it, and you miss the ball anyways; at most they would give you a warning for “unsportsmanlike conduct”.
Since ping pong is a game, hitting the net on purpose would be called “game tampering”. If you’re playing for money or bragging rights then that’s another story.
The first player to 21 wins by leading after two equal periods of play. The receiver at the beginning of each period may choose either an advantage or a service. The first player to win two periods wins the game. A tie is possible if both players score 10 points in one period, and then each player has one more point after deuce (40-40). In competition play such as at the Olympics, a match consists of the best of five games.
In table tennis there are no walls or ceilings involved which makes net play a big part of the game. In order for the ball to be ruled good it must first completely cross the vertical plane of the net and land in the proper half of the opponent’s side of the table.
If you hit a net shot with spin, either backspin or topspin, then depending on which spin you used and the speed of your shot, you can either bring the ball down into your opponent’s court or have it go over his head.