well there are a few but mostly its monsters effects that let you attack twice for example:elemental hero wildege and ultimate tyrano
"Double Attack" is one spell card that does it.
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I run a very good dragon deck and the only equip card I run is Axe of Despair. 1000 attack.
There are 3 Spell Cards in the TCG that change a monster's type: the Equip Spell "Dragonic Attack", which changes the equipped monster into a Dragon; the Equip Spell "Reptillianne Rage", which changes the equipped monster into a Reptile; and the Field Spell "Zombie World" which changes all monsters in play and in the Graveyards into Zombies.
yes you can equip spell card cards to an opponent's monster unless the card states so a good example of this is snatch steal
Only the Spell card Darkness Approaches can flip a monster into face-down Attack position. By discarding two cards, Darkness Approaches lets you flip one face-up monster face-down without changing the battle position (so a monster may end up in face-down Attack position).
Monsters who go into the S/T zone for any reason are then treated as Continuous Spell Cards or Equip Spell Cards depending on what it is doing. It is no longer a monster card so is unaffected by anything that specifically affects monster cards, and cannot be tributed for a tribute summon, etc. However if something required you to send an Equip Spell Card to the graveyard, you could use that monster.