**Dragon-type Pokemon are resistant to Fire, Water, Grass, and Electric attacks because they're elemental. Those four elements are kind of like the original four elements: wind, water, fire, and earth. Dragons can be master of any one of those four elements, hence why they're resistant to those Pokemon types.
**The reason why Electric attacks are strong against Flying-type Pokemon probably relates to Benjamin Franklin's experiment with flying a kite in a thunderstorm...
**Fire attacks are strong against the Steel-type because metals conduct heat well. (In that case, shouldn't Steel-types be weak against electricity too? Metal also conducts electricity well.)
**About Dark prevailing over Psychic: Many people who divine the future and foresee a terrible omen (Dark) are haunted by it, and thus they are the first ones to suffer from the omen. Thus Psychic-types are weak against Dark attacks. Also, if the omen's in the future, psychics can do very little if anything to stop the omen from happening, hence psychic attacks' weakness against Dark-types.
**About Ground attacks' strengths: Dirt is often used to put out fires, whether normal or electrical. This explains Ground attacks' strengths against Fire and Electric-type Pokemon. Also, some soils neutralize acid rain, hence Ground attacks being super-effective against Poison-types and Poison attacks being weak against Ground Pokemon. Earthquakes break up the land (rocks), so that's why Ground attacks are strong against Rock-types.
**Normal and Ghost attacks are ineffective against each other. This is because ghosts can't affect or be affected by the physical world.
**However, ghosts CAN influence the minds of people (and that's why people "see" them or are "possessed" by them), and that's why Ghost attacks are super-effective against the Psychic-type.
**I think Ice attacks are super-effective against Dragons for two reasons: First of all, most dragons can fly, and if Flying Pokemon are weak against ice, so are Dragons. Second, dragons, no matter how magical, are still reptiles, who stop moving when the temperature gets too cold. Thus dragons are sensitive to ice.
**Poison attacks are super-effective against Grass-type Pokemon because of the way pesticides can poison plants (and that's why it's better to eat organic produce). Speaking of pesticides, that was originally the reason why Poison attacks were super-effective against Bug Pokemon, but I guess people later realized that bugs could over time develop resistances to bug repellants, so Poison attacks were made neutral in that case.
**OK, here's one I don't agree with: Dark prevails over Ghost. Why? It should be the other way around. Ghosts are mainly seen at night, and they are usually seen as possessing many dark qualities themselves--don't you think that for these reasons ghost Pokemon should be strong against the Dark-type?