Are there secret combos or attacks?

As of update 1.0.8, Ryu, from the Street Fighter series, is available as a paid downloadable character. Uniquely among the characters in the game, he has the non-obvious command inputs you allude to, all of which are variations on his Special Moves:

• Hadoken: Neutral special (Special button alone). Shoots a slow-moving blue energy projectile.
  • Input Hadoken: Quarter-circle forward (down, down-forward, forward + Attack or Special button). Projectile is slightly larger and 1.25 times stronger.
  • Shakunetsu Hadoken: Half-circle forward (back, down-back, down, down-forward, forward + Attack or Special button). Projectile is red, has a flame effect, and hits multiple times on contact before exploding.
  • When Kirby copies this move, he too gains access to these input variations.
• Tatsumaki Senpukyaku: Side special (forward or back + Special button). A spinning kick that slows descent when airborne.
  • Input Tatsumaki Senpukyaku: Half-circle backward (forward, down-forward, down, down-back, back + Attack or Special button). Kick lasts longer, faster, and 1.16 times stronger.
• Shoryuken: Up special (up + Special button). An uppercut.
  • Input Shoryuken: "Z" input (forward, down, down-forward + Attack or Special). Increases power; Ryu gains invincibility until he starts to fall and receives no landing lag when he touches down.
• Focus Attack: Down special (down + Special button). Stuns opponents with a charged punch.
  • There are no input variations, but you can cancel the attack by forward, forward or back, back. If done after hitting the opponent, they'll still be stunned, but you'll end the animation sooner.

If that's not enough, Ryu also has unique move variations (on all of his Attack and Special moves) depending on whether you tap or hold the appropriate button - holding generally makes the move stronger.

All attacks in Super Smash Bros. are performed with a directional input and one button. You can sometimes chain these moves together to form combos, but there are no multi-button input combos like you're imagining.

Most forward smashes (control stick forward + A simultaneously) can be angled up or down by starting the attack by moving the stick forward, but then moving it up or down before the move finishes. This might not be obvious to players at first. Usually the attack is the same, just angled a little bit up or down instead of straight forward.

Little Mac is unique in that his angled forward smashes are actually entirely new attacks with new animations and properties - Standard forward smash is a powerful forward punch, up-angled forward smash is an uppercut with vertical knockback, and down-angled is a low sweep that does high shield damage but low knockback. That's the only case of "secret" attacks I can think of.