Abra : Magicians often use "abracadabra" as a magical chant, so Abra's the first part of the phrase.
Aerodactyl : Aero means as in flight, and dactyl was taken from pteroDACTYL.
Alakazam : Alakazam is a phrase often used in magic tricks.
Arbok : Backwards of cobra, but spelt with a 'K'.
Arcanine : From canine.
Articuno : Artic is equivalent to ice, whilst uno is Spanish for 1.
Beedrill : It's a bee, 'nuff said. ^_-
Bellsprout : Its head is shaped like a bell and it's a sprout!
Blastoise : From tortoise.
Bulbasaur : Bulb and dinoSAUR combined.
Butterfree : Butterfly!
Caterpie : From caterpillar.
Chansey : Catching this Pokémon is up to chance.
Charizard : CHARcoal and lIZARD.
Charmander : CHARcoal and salaMANDER
Charmeleon : CHARcoal and chaMELEON.
Clefable : Uhm...it's a fabled Pokémon, I guess, since its Pokédex entry notes it as "rare".
Clefairy : It's a fairy!
Cloyster : A play on 'Oyster'.
Cubone : It's a bone!
Dewgong : A play on 'Dugong'
Diglett : Perhaps it likes to dig?
Ditto : Hmm...I don't know this one!
Dodrio : It has three heads...hence the 'trio'.
Doduo : It has two heads, hence the 'duo'.
Dragonair : It's a dragon!
Dragonite : It's still a dragon!
Dratini : Since it's Japanese name is "Miniryu", then I guess it's name means Tiny Dragon.
Drowzee : It makes people drowsy.
Dugtrio : Something like Diglett, except there's three of them now and they call it Dugtrio!
Eevee : Abbreviation of "evolution"
Ekans : Snake spelt backward(my, aren't Nintendo clever?)
Electabuzz : Electrical buzz ^_^
Electrode : Hmm...I don't know this one either
Exeggcute : It sounds like "Eggs are cute". o.O
Exeggcutor : This sounds like "Eggs are cuter". O.o
Farfetch'd : Another name that doesn't make sense. o.O
Fearow : A play on Sparrow.
Flareon : Flare means light up.
Gastly : It's made out of gas and gastly also means ugly.
Gengar : Another name that doesn't make sense.
Geodude : Geology is the subject of studying rocks and dude is slang for cool guy.
Gloom : Probably it has its eyes closed all the time looking sad?
Golbat : It doesn't make sense. o.O
Goldeen : A play on goldfish.
Golduck : It doesn't make sense either. o.O
Golem : Golem is the name of a ancient rock creature.
Graveler : Gravel probably means rock.
Grimer : Grime means dirty stuff.
Growlithe : Probably it likes to growl. ^_^
Gyarados : Still doesn't make sense!
Haunter : It's like a poltergeist that haunts your house.
Hitmonchan : Chan is taken from Jackie Chan.
Hitmonlee : Lee is taken from the late Bruce Lee.
Horsea : A seahorse. ^_^
Hypno : Taken from HYPNOtise.
Ivysaur : Poison IVY and dinoSAUR combined.
Jigglypuff : Probably it's jiggly and it's a puff.
Jolteon : Jolt is what you'll receive from an electrical shock.
Jynx : Taken from the word 'jinx'.
Kabuto : ...
Kabutops : ...
Kadabra : Same as Abra's, but it's the last word of the phrase "Abracadabra".
Kakuna : A play on cocoon.
Kangaskhan : A play on kangaroo.
Kingler : Probably it's king of the sea? o.O
Koffing : A play on coughing.
Krabby : It's a crab, for gee's sake!
Lapras : To lap up water?
Lickitung : Lick and toungue. ^_^
Machamp : It's a champion, for gee's sake!
Machoke : Probably it likes to choke people?
Machop : Probably likes to chop people?
Magikarp : Karp is taken from carp...as for the magi...I don't know, but it probably means magic, since the worthless thing evolves into the superior Gyarados!
Magmar : Magmar is another word for lava.
Magnemite : Magnet.
Magneton : Magnet.
Marowak : A play on bone marrow.
Mankey : It's a monkey.
Meowth : A posh version of 'meow'.
Metapod : From pod.
Mewtwo : It's created after Mew. ^_^
Moltres : Molt comes from volcanoes and tres is the spanish number for 3.
Mr. Mime : It likes to mime.
Muk : Muck is something like mud.
Nidoking : Needle and king.
Nidoqueen : Needle and queen.
Nidoran (F) : Needle.
Nidoran (M) : Needle.
Nidorina : Needle.
Nidorino : Needle.
Ninetales : Because it has nine tales, for gee's sake!
Oddish : From raddish.
Omanyte : ...
Omastar : ...
Onix : It's a play on Onyx, which Onyx is a type of stone. Paras : A play on parasite.
Parasect : A play on parasite.
Persian : A Persian is a type of cat.
Pidgeot : From pigeon.
Pidgeotto : From pigeon.
Pidgey : From pigeon.
Pikachu : Pika is a type of rat...as for the 'chu'...
Pinsir : Pincer.
Poliwag : HMm...
Poliwhirl : ...
Poliwrath : ...
Ponyta : It's a pony, for gee's sake!
Porygon : Porygon is a play on polygon, which is a shape.
Primeape : A play on primate.
Psyduck : It's a psychic duck!
Raichu : ...
Rapidash : Rapid means fast, and ash is the remains of anything burnt.
Raticate : A play on rat.
Rattata : A play on rat.
Rhydon : A play on rhinoceros.
Rhyhorn : A play on rhinoceros.
Sandshrew : It's a shrew.
Sandslash : See those claws? Yup, those claws can slash anything.
Scyther : A scythe is a curved blade, and Scyther's arms are probably like that.
Seadra : SEA DRAgon.
Seaking : It's king of the seas...?
Seel : It's a seal, for gee's sake!
Shellder : A play on shell.
Slowbro : It's still slow, and I think they regard the parasite on its tail as Slowbro's brother.
Slowpoke : It's what people call people who are slow. And no doubt Slowpoke is slow!
Snorlax : It's a combination of snore and relax.
Spearow : A play on sparrow.
Squirtle : It's squirtle and turtle combined(see his tail? It's like a squirrel's).
Starmie : A starfish.
Staryu : A starfish.
Tangela : Because it's tangled!
Tauros : A play on Taurus, which is a Zodiac Sign that resembles a bull.
Tentacool : A play on tentacle.
Tentacruel : A play on tentacle.
Vaporeon : Water vapour.
Venomoth : Venomous mouth. ^_^
Venonat : It's a venomous gnat!
Venusaur : Venus-fly-trap combined with dinosaur.
Victreebell : It's a victorious bell! ^_^
Vileplume : Plume is a type of flower, and probably it has a vile smell.
Voltorb : It's a round-shaped Pokémon and volts are electrical stuff.
Vulpix : Vulpes is the scientific name for foxes, and ix comes from six. ^_^
Wartortle : Must be a play on turtle, and combined with war.
Weedle : A play on needle.
Weepinbell : A weeping bell?
Weezing : We wheeze when we have a stuffy nose. ^_^
Wigglytuff : It's wiggly and it's tough.
Zapdos : Zap has a relevance with something electrical and dos is spanish for two. ^_^
Zubat : It's a bat!

That was hard to type...o.O *groans*

Those with the '...' means that the name doesn't make sense, or there's nothing related to it. ^.^ Please don't hurt me! *ducks*