BestDragon - Dragon has only two weaknesses (itself and Ice) but multiple resistances which can make them rather hard to take down. But what makes them really shine is that only Steel resists Dragon so they're usually swinging for big damage even though most of their moves are only of moderate power (or have low accuracy or negatively effect the user in some way).
Psychic - Psychic not only has some incredibly powerful attacks, it also has lots of extremely powerful Pokémon. As a result resistance generally doesn't help much so only Dark-types have a reasonable chance of surviving a hit from a Psychic.
Dark - Dark's best attributes are it's immunity to and effectiveness against Psychics. But Dark-types tend to have low defenses and are thus glass cannons. Also, Dark-type moves are fairly low-powered compared to most other types but tend to have more side-effects (flinching, defense lowering, etc) as a result.
Ice - Ice is by far the easiest way to take down Dragons and a lot of them have a chance to freeze the opponent which renders the target incapable of doing anything. Ice-type Pokémon, however, have one major problem: multiple weaknesses and only one resistance (Ice) make them fairly weak defensively.
Ground - Ground-types are immune to electric but can't hit fliers so it's a bit of trade-off. What makes Ground really good is that is super-effective against FIVE! different types (and attacks like Earthquake and Magnitude which can one-hit kill anything that's weak to ground and severally injury most everything else don't hurt).
Steel - Steel-types aren't the hardest hitting lot but their resistance to nearly everything makes them useful as tanks while you heal up the rest of the party.
Fighting - Strong against both Dark and Steel but only weak to Psychic and Flying. Not surprisingly, Fighting-type Pokémon tend to have fairly high Attacks which, when combined with Fighting's super-effectiveness against five different types, makes it a force to be reckoned with.
WorstBug - Bug is strong vs psychic and dark. And that's about all it has going for it. While Bugs have finally received some higher-powered attacks most Bug Pokémon still have fairly low attack values and thus still deal only moderate damage.
Normal - Immune to ghosts but can't hit them either; weak to fighting; resisted by rock and steel. Poor Normals; they're probably the most common type yet one of the least useful overall.
Poison - First off: I love my Crobat and my
Flying, Water, Fire, Grass, Ghost, Electric, Rock don't really stand out as particularly good or bad thus they're not in either list.
Now obviously a list like this is going to vary from person to person (an ask five people and get six responses kind of thing) so feel free to post your own lists. I'd love to see them.