Water and Ice are my favorite types, as you can see by my username and avatar. I used all types though when I played the games. Sure, they have their weaknesses, like Water is weak against Electric and Grass and Ice is weak against Fire, Rock, Steel and Fighting, but they are the unsung types and very powerful if you train them right. I was excited to find there is a Dragon/Ice type named Reshiram that seems nearly indestructable.
I think the most powerful types are Dragon, Ghost and Psychic types, with Fire and Dark coming in close. Dragon only has 2 weaknesses (itself and Ice) and are harder to take down due to their stats. Ghosts are immune to Normal and Fighting and have super effectiveness against other Ghost-types and Psychic-types and are only weak against other Ghosts and Dark-types. Psychic-types were untouchable during Generation I. Fire-types have a wide range of powerful moves that can overwhelm most of the types. Dark-types are only weak to Bug and Fighting but deal critical damage to Ghost and Psychic-types.
It's hard to say which type is the best though, as they all have advantages and disadvantages. Another factor is mixing types together, like Dark/Ghost (Sableye) and Ghost/Dark (Spiritomb). They have no weaknesses because the Ghost aspect won't allow Fighting moves to target them and their Dark attribute keeps Psychic moves from targeting them. They also resist Poison moves and are damaged normally by all the other types that can still hit them. Tynamo and its evolutionary line also have no weaknesses because of their Levitate ability, which does not allow Electric's sole weakness, Ground, to hit them, and all other types either damage normally or are resisted.