For example, I normally only catch 8 pokemon, using 2 of them as HM pokemen.

I like to pick 6 and collect and use them as I go. For instance: I always have to have a Hoothoot and look for it first. Then I think about what I want next and go for it. I will collect everything else along they way but I make a quick trip to the PC to deposit the ones I do not want.

I usually have 2 "HM whores" and 4 elite pokemon

I usually just get my first pokemon and get the cool looking or the ones i know will be good which is whenever they show up. For instance i didnt have a 3rd pokemon till after the 4th gym in Pearl. (which was the latest game for me. :P)

Well first I put some peanut butter on my balls and....
 
Oh...you mean...

" I usually just get my first pokemon and get the cool looking or the ones i know will be good which is whenever they show up. For instance i didnt have a 3rd pokemon till after the 4th gym in Pearl. (which was the latest game for me. :P) "

Usually a tank, 2 sweepers, and a baton passer. And something to use fly.

I mix my HMs into my good pokemon. Why not? Lets me have more good fighters. I also just try to keep the basic elements covered, and I love hybrid-type pokemon. I'll be super effective with SOMETHING or another, and I usually try to keep them slightly overlevelled. 

The optimal way of doing things is taking one HM Pokemon (with a limitation of 4 moves, the optimal way is to take different Pokemon depending upon the circumstances and what you know you'll be needing), and 5 "real" Pokemon.  Surf is the big exception, since it is among the best water-type moves to begin with.

i usually have my starter and a varied array of different pokemon types, like if i pick charmander, i don't catch a pidgey, because then i know my charmander is going to evolve into a charizard and i can teach fly to it instead, also because i'm lazy and don't like having to raise more pokemon than i need, thats why i always finish the game at like 40-50, and usually only my starter is at 60, cause i mostly only use my starter to fight with. i also never get HM slaves, cuse they seem boring.
 
well, at least that's what i used to do, so far i've moved on from pokemon and WOW to more actually RP-like RPGs.

i try to catch anything i come across that i haven't already, and i generally try to have a fire type, a water type, an electric type, and then my fourth will be determined by the secondary types of my fire, water and electric pokemon. it's usually a psychic type, unless i have, say a Golduck, at which point i try to have something that has a very open learnset, and really good stats like Kangaskhan or Mightyena

i try to avoid having HM whores and slaves by having my "assault" Pokemon know at least one HM move. But before deciding which assault should know which HM, I look up their move charts.

I catch them by THROWING A POKEBALL TO THE FACE!
 
And just train 6 mains and 2-3 HM Pokemon.
 
I do train some counter picks for the elite 5 too though.

I'm old school.  I duped myself a near-infinite supply of master balls.

" I'm old school.  I duped myself a near-infinite supply of master balls. "

The way I see it is you get a pokemon and then go for a 20 mile run with it, boom ultimate pokemon.

For HeartGold, I'm going to select 6 Pokemon before I play it (making sure I can use every HM, and cover a number of types) using Bulbapedia, and catch just those as I make my way through the game. Well that's what I'm planning on doing. Any legendaries I come across that appeal to me more then any of my 6 Pokemon will be swapped in. 
 
I love Bulbapedia, though I do wonder if I would enjoy the Pokemon games even more if I didn't know when and where I would come across every Pokemon in the game. I can't help myself from doing my research. Yeah, I'm keen.

I have one Lv. 100 tank, one flyer, and 4 randoms to use Exp. Share on them to evolve them.

find grass, grind grind grind, find higher level grass, grind grind grind, repeat

I like to have six pokemon in my party and I like to keep it that way throughout my adventure. 
Along the way I also capture any pokemon I don't have of the earliest evolvement stage and then evolve/grind them after the main quest when I have nothing better to do.

i started by getting 5 pokemon but found myself underleveled pretty soon. so i dropped one and picked a 5th one back up before the elite 4 and leveled it with the EXP-share item... 

" The way I see it is you get a pokemon and then go for a 20 mile run with it, boom ultimate pokemon. "

Me? I've decided to take the insane route. I am going to train six Pokémon, all equipped with everstones and leveled up to around 60. I will then use these six unevolved Pokémon to wreak havoc against the Elite 4. My choices? Rotom, Magby, Pidgey, Geodude, Machop, and a wildcard slot. 
 
And it will be GLORIOUS.