If I have a equipment and I try to equip it to my creature, my opponent got a spellskite, can he switch the target of my equipment to his spellskite
{Spellskite}
Yes, it can change the target to itself, but the equipment will not equip to spellskite unless you control it:
702.6a (http://imtgapp.com/forum/index.php?action=imtg;area=rule;number=702.6a): Equip is an activated ability of Equipment cards. "Equip [cost]" means "[Cost]: Attach this permanent to target creature you control. Activate this ability only any time you could cast a sorcery."
If you didn't control the spellskite, it would change the targeting to itself. But since you do not control it, the equipment would not equip itself to spellskite
He can do it but since it's an illegal target your equipment will still equip to your target.
He is wasting his time trying to do that....more or less.