In D&D 3.0 and/or 3.5 -- can Dispel Magic or Mordenkainen's Disjunction dispel Supernatural effects? (For instance, a druid's wild shape.)
In 3.5, no
Supernatural abilities are not subject to dispel magic per the definition of supernatural abilities:
Supernatural abilities are magical and go away in an antimagic field but are not subject to spell resistance, counterspells, or to being dispelled by dispel magic. Using a supernatural ability is a standard action unless noted otherwise. Supernatural abilities may have a use limit or be usable at will, just like spell-like abilities. However, supernatural abilities do not provoke attacks of opportunity and never require Concentration checks. Unless otherwise noted, a supernatural ability has an effective caster level equal to the creature’s Hit Dice. The saving throw (if any) against a supernatural ability is:
Emphasis mine. Mordenkainen's disjunction is slightly less clear, because it opens by saying that all magical effects are affected, but it goes on to detail exactly what it does to effects in its area:
All magical effects and magic items within the radius of the spell, except for those that you carry or touch, are disjoined. That is, spells and spell-like effects are separated into their individual components (ending the effect as a dispel magic spell does), and each permanent magic item must make a successful Will save or be turned into a normal item. An item in a creature’s possession uses its own Will save bonus or its possessor’s Will save bonus, whichever is higher.
As the spell has no provisions for affecting supernatural abilities, and references dispel magic as its method of removing them, you can't disjoin a supernatural ability's effect.
In 3.0, yes
According to the errata to the 3.0 Dungeon Master's Guide (findable here), supernatural abilities can be dispelled in that edition:
Supernatural Abilities (Su): Supernatural abilities are magical but not spell-like. This far-reaching category includes the basilisk’s petrifying stare, the monk’s ki strike, and the ghoul’s paralytic touch. Supernatural abilities are not subject to spell resistance and do not function in areas where magic is suppressed or negated (such as an antimagic field). A supernatural ability’s effect can be dispelled if the duration is longer than instantaneous, but a supernatural ability is not subject to counterspells.
If you're playing in 3rd edition D&D instead of 3.5, then a supernatural ability can be dispelled. However, you might run into issues with many supernatural abilities not having caster levels. I sadly do not have access to the 3.0 monster manual to check, so I don't know for sure if the definition of supernatural abilities includes the same text about caster level being equal to the creature's Hit Dice.