Due to the change in Pokemon in this game, certain trainers are easier or harder. Here's a guide to some of them.

a) Brock

Pikachu can't do anything against Onix or Geodude! (That hurts anyway) So, get a Caterpie, evolve it to Butterfree and use Confusion on them both, and they'll be dead in no time! Another option people are telling me is to use Mankey, but I never found a reason to. Butterfree destroys them.

b) Misty

Very easy to beat. Pikachu = Electric. Misty's Pokemon = Water. And electric beat water.

c) Lt. Surge

Lt. Surge's Raichu is very tough. It uses Thunderbolt, and Mega Kick/Punch (could be either). Can it do a Body Slam? Unsure (it hits Pikachu with two on TV). Anyway, here are some suggestions:
a) I use my Butterfree. It's fast enough just to go before Raichu and I use Sleep Powder. There's about a 50% chance of it affecting him I have found. After that, just keep smashing him with Confusion, hoping he does not wake up. This should do quite well. My Butterfree was Level 29.
b) Use Diglett or Dugtrio, making sure either of them are over level 20. Keep using the Dig Attack and Raichu should lose within a few hits.
c) Do the same as above with Geodude (you will have to teach him dig).

d) Erika

Erika has had a change of Pokemon. Erika uses Weepinbell, Tangela, Gloom. (If you remember, she used those on the TV show). Seems to me like she is worse in this (on the Blue/Red she has Vileplume and Victreebell instead of Gloom and Weepinbell).

e) Koga

Koga uses four Pokemon, starting with three Venonats. They increase in levels, 40, 42 and 46. They all use Toxic (TM 06). His final Pokemon is a level 50 Venomoth! You should use Charizard with Slash or Ember, or a Scyther with Sword
Dance and Slash. Psychic attacks and "Rock Slide" are also helpful. (If you remember, Koga used Venonat/moth in the cartoon, but he did have Golbat too). In the original game, Koga used Koffing, Muk, Koffing, Weezing.

f) Sabrina

Originally she used Kadabra, Mr. Mime, Venomoth and Alkazam. Now she has gone all psychic and uses Abra, Kadabra, and Alkazam!
Abra: L50 Teleport, Flash, and i think Psywave
Kadabra: L50 Psywave, Recover, Psychic, and Kinesis
Alakazam: L50 Reflect, Psywave, Psychic, and Recover
My suggestion is to use Gyrados and attack Alkazam at least with Surf. I don't know why, but at the end of the game, when Gary Oak used his Alkazam, my Gyrados always puts it out with one hit using Surf. (If you remember the TV show, Sabrina uses Abra, but it evolves into Kadabra during the fight. Totally against the game....

g) Blaine

Blaine has Growlithe, Rapidash, Ponyta, and Arcanine. However, he uses the following now:
L48 Ninetales: Uses Confuse Ray, Flamethrower, Tail Whip, and Quick Attack.
L50 Rapidash: Uses Take Down, Fire Spin, Stomp, and Growl.
L54 Arcanine: Uses Take Down, Reflect, Flamethrower, and Fire Blast.

h) Giovanni

L50 Dugtrio: Uses Earthquake, Sand Attack, Dig, and Fissure.
L53 Persian: Uses Fury Swipes, Double Team, Screech, and Slash.
L53 Nidoqueen: Uses Thunder, Earthquake, Tail Whip, (unsure if it has 4th attack)
L55 Nidoking: Uses Thunder, Double Kick, Earthquake, and Leer.
L55 Rhydon: Uses Fury Attack, Earthquake, Horn Drill, and Rock Slide.

The only difference being that he has a Persian instead of a Rhyhorn. Gyrados or flying Pokemon will defeat Dugtrio easily. Fighting Pokemon (Hitmonlee Rolling Kick) should defeat Persian no trouble. Nidoqueen and King are hard. The best strategy is to use Hypnosis or other forms of sleep, and then Dream Eater if available.. Rhydon can be taken down easily with water attacks.