The other day, while playing, my friend triggered Glimmervoid Basin, which gives each player a token which is a copy of a targeted creature (except the creature's owner). He chose to copy the Noggle Hedge-Mage, which has two enters-the-battlefield abilities. The question is: when these copies are generated, do they trigger the enter-the-battlefield abilities? Do token-copies "enter the battlefield?"
Yes, the enter-the-battlefield ability will trigger.
701.6a To create one or more tokens with certain characteristics, put the specified number of tokens with the specified characteristics onto the battlefield.
When a token is created, it enters the battlefield. In the case of Glimmervoid Basin, the token's characteristics are defined by the creature it is copying, which includes any abilities it has.
706.2. When copying an object, the copy acquires the copiable values of the original object’s characteristics [...] The “copiable values” are the values derived from the text printed on the object (that text being name, mana cost, color indicator, card type, subtype, supertype, rules text, power, toughness, and/or loyalty), as modified by other copy effects, by its face-down status, and by “as . . . enters the battlefield” and “as . . . is turned face up” abilities that set power and toughness (and may also set additional characteristics). Other effects (including type-changing and text-changing effects), status, and counters are not copied.
For simple proof, the card Anointer Priest has a triggered ability that is triggered only when creature tokens enter the battlefield, so creature tokens must enter the battlefield and trigger 'enters the battlefield' abilities, or Anointer Priest makes no sense.
Gendolkari covered the exact rules involved, so I won't repeat them.
It's worth noting, though that when Noggle Hedge-Mage's ability says "When Noggle Hedge-Mage enters the battlefield", it is specifically referring to itself, and each copy will be referring to their selves.
201.4. Text that refers to the object it’s on by name means just that particular object and not any other objects with that name, regardless of any name changes caused by game effects.
The full sequence:
Glimmervoid Basin's ability goes on the stack targeting Noggle Hedge-Mage
Basin resolves, creating N-1 noggles (where N is the number of players)
All the noggles' "enters the battlefield" triggers trigger and are placed on the stack in "active player, non-active player" order. That means that your friend (assuming he has a noggle and the requisite lands) will place both his abilities on the stack (in whichever order he chooses, choosing targets for both). Then the next player in turn order with a noggle (and the requisite lands) will place their triggers on the stack in either order, choosing targets for both. Repeat until all triggers have been placed on the stack. All of the noggles will be viable targets for the "tap two permanents" trigger.
Active player gets priority, and may activate abilities and play spells.
Once all players have passed priority, the stack starts resolving like normal.