If somebody plays a wild card (without +4), is the next person's turn skipped?
No, it does not skip your turn. There is a separate card called “Skip” that does that, Wild only allows you to change the color being played. 

From the rules:


  Wild Card - When you play this card, you may change the color being played to any color (including the current color) to continue play. You may play a Wild card even if you have another playable card in hand. If this card is turned up at the beginning of play, the person to the left of the dealer chooses the color to begin play and plays the first card. 


Nothing about skipping a player is mentioned.