The Dragon #298 Sage Advice column "Official Answers to Your Questions" includes this exchange:
Can undead, which lack metabolisms, use potions, which require ingestion? I believe undead can use magic oils, which are applied externally.
Potions require swallowing, not ingestion. Any corporeal creature can use a potion (see page 191 in the Dungeon Master’s Guide ), provided it can swallow. Anything with an intact throat can swallow. Some DMs say skeletal creatures cannot swallow, others say they can. Check with your DM. Any corporeal creature can use an oil. (113)
The Sage at the time is Monster Manual (2000) author and D&D Third Edition co-designer Skip Williams. This ruling predates the Dungeons and Dragons 3.5 revision but to my knowledge was never further clarified or later contradicted.
This ruling jibes, by the way, with Potions on Activation that, in part, says, "A creature must be able to swallow a potion…. Because of this, incorporeal creatures cannot use potions or oils. Any corporeal creature can imbibe a potion" (DMG (2003) 229).
Note: In this DM's campaigns, skeletons can totally drink—therefore benefit from—potions because that's hilarious.