The dispel has a magnitude that must be higher than that of the spell that was cast. More info here: http://www.uesp.net/wiki/Oblivion:Dispel
My character primarily uses dispel on self in a few ways:
She has a dispel 100 on self spell that she uses when she wants to extinguish her own light or night eye spells (because they are each 120 seconds and she normally doesn't need them that long - just for a quick search). She can also use the spell on herself to evaporate her own summon if, say the summon gets into a friendly fire argument with an ally.
She also carries very strong homemade dispel potions (she is an alchemy master so their strength is 111 and her preferred recipe is bergamot + graqes). A mage is in trouble if silenced, and silence prevents you from casting the dispel effect to eliminate the silence. So, the answer is to quaff a potion to eliminate the silence effect. As long as she can cast, she can use spells for any effect - therefore she finds the dispel potions invaluable.
She also has a dispel 100 (on others) on target spell but we have mixed results. It should, when cast on a summoner, cause his summon to evaporate - but it doesn't alway seem to work.