I'd like to contribute a few sections on how to vary Pikachu's approach.
Now, Anther is the king of varied approaches, and all of this is stuff that he does regularly, so none of the credit really goes to me.
Pikachu, IMO, has the best, most versatile approach in the game.
One thing that makes it so good is that he doesn't feel floaty. Play Luigi, G&W, or even MK and you'll notice that Pikachu's short hop is actually short and his fast fall is actually fast. This is one of the major keys to Pikachu's approach - being so very fast.
The second thing about his approach that its many, many times more useful than anyone else's approach. This is because they lead into Pika-combos (they aren't real combos, but they're pretty close). Fast falled fair to (grab, usmash, utilt, etc) is a good example, but often a dsmash leads to a thunder, an upair leads to a fair (which leads to an uptilt...) etc. Don't even mention how much damage a grab can mean. How many other characters can string together attacks as easily?
Now, to the approaches themselves. Lets start with the standard approach:
--- full hop fast falled fair ---
This is a great approach because pika's fast fall is fast enough that it becomes hard(er) to time the shield grab, and the full hop allows you to space it correctly so that you land behind the opponent. This is also a great approach because it leads to grabs or combos and has so many variants that can really screw with an opponent's head. I'll list a few below:
---full hop fast fall dsmash---
This is a great counter to the shield grab. The opponent is expecting you to ffair and wants to grab you - throw this in. You can replace dsmash with grab, uptilt, upsmash, a spaced fsmash, a spaced thunderjolt, a neutral air, etc for even more variety. Dsmash and grab are most effective though because the opponent is most likely shielding.
---full hop fast fall airdodge---
if the opponent likes to attack you while you're coming down, or if you want added safety, throw this in. Its great because right after you fast fall and airdodge, you become invincible at about the range of a short hop. After you land you can do anything above. Watch out for pesky MKs or Robs who like to sit in their shields and punish everything with a dsmash.
---full hop fast fall full hop---
this is from the melee days, and it still works wonders. I don't have much to say here except try it out if you've never done it before.
---full hop QAC reset ---
full hopped into a bad position? QAC to reset it! throw in a thunderjolt afterwards for kicks.
Now that's for the full hop. I know lots of Pika players still live on the short hop - its alright, I have mindgames for you too. The short hop has 2 very great properties - the fast fall is VERY fast, and autocancelling works. I don't recommend autocancelling because it slows down your approach and makes you more predictable to be punished, but mindgames make up for it.
---sh ffair---
Ah, the short hop. Once a staple in the smash community, now it is too slow to be spammed thoughtlessly. Everyone and their swords have forward smashes which just eat through these approaches, and grabs are too easy to time. Its not dead yet, though. sh ffair is still a very effective approach if combined with the following mindgames below:
---sh fast fall dash --- *circle dashing*
The best use of this is to space it so that you sh, fast fall (just out of grab reach), and dash grab them. This is very fun to do.
---sh fast fall dsmash---
again, this shouldn't go to waste.
---sh airdodge---
This is somewhat slow, so I wouldn't recommend pulling it out unless your opponent has a tendency to attack through your approach in stead of shield it. Master the timing of this so that you can dsmash or dash grab as soon as you hit the ground.
---sh QAC---
At the peak of your sh, your horizontal QAC should still go through most taller opponents. This is a great way to poke at the enemy or just fly around his head until he gets pissed off and starts smashing randomly in different directions.
Finally, we have the ground approach. The best ground approach is a dash grab, but because of the properties of the shield, we can abuse it to pull out more mindgames. The ground approach can also be mixed up with the short hop or full hop approaches at any time.
--- dash grab---
You'd be surprised how effective this sometimes is. Just run in and grab them. Easy, right?
--- dash shield---
You'd sometimes see this in high level melee play back in the day. Dash until you're right outside grab reach and put up your shield. You can then do several things:
a) dash grab
The shield drop timing is short, so abuse it. Drop your shield, and dash grab.
b) sh hop ffair
If you think he's going to whiff a grab, this is a perfect counter.
c) fsmash
if you're in range, it is also a good counter to a whiffed grab. If you're slightly farther away, its a good counter to opponents who try to dash (or mortar slide) into you.
d) full hop thunder jolt
This is actually deserves its own section as an approach because it is awesome.
---full hop thunder jolt---
This is a great tool against aggressive opponents. The minute they move in on you, throw this in their face. If you haven't been spamming it all game, it really messes up their rhythm.
Thunderjolt works best when you're about a platform length or 2 away from your opponent. At this distance, both you and your opponent are sitting around wondering who's going to approach first. Try full hop thunderjolting. Chances are your opponent has just decided to move in to attack you and receives a face full of awesome projectile. Feel free to follow up with a dsmash or grab.
That's about all of my approach variation mindgames. Pikachu has the best approach in the game and should be abused readily. One more thing I'd like to add -
---Don't QAC nair for a standard approach!---
QAC nair is NOT a good approach because it is defeated by shield camping. All of the approaches above actually do well against shields - this one doesn't. QACing works well well if you 'poke' them continually while staying beyond their reach, but it shouldn't be used as an approach as much. Throw it in every once in a while if your opponent doesn't shield very well - it looks good on combo videos.