There are not many cards that have abilities that work if they are in your opening hand, but there has been a large increase in the last year. Five were printed in Magic 2011, the Leylines, of which four are new, and five Chancellors were printed in New Phyrexia.
All of these cards work after players have chosen their starting hand. In other words, after all players have resolved mulligans. You cannot reveal a Leyline of Lifeforce, put it into play and then mulligan your hand.
Like many things in Magic, revealing these cards in hands take place in APNAP (Active player, non-active player) order. Technically speaking, there is no active player at this point, so the starting player is treated as the active player. This player will reveal all cards with abilities like these and either generate the effect or put them into play then the next player in order will do the same.
The Chancellor cards do not enter play at the beginning of the game, they generate an effect. (For example, Chancellor of the Tangle) You can only take advantage of each individual Chancellor card once per game. To make sure that players are playing properly, players will need to reveal and keep revealed all of these cards until the first turn of the game actually starts.