I realize that we already have an accepted answer, and the actual answer wasn’t from 3.5e to begin with, but for the sake of completeness, we also have a list of intelligent oozes from D&D 3.5e:
Intelligent oozes, including gelatinous cubes—not officially playable
One of the hard, practical stops on playing any monster is Intelligence—even if you ignore the rules saying you’re not allowed to play one, you can’t really turn a mindless creature into a player character. Most oozes—including the gelatinous cube—are mindless, but D&D 3.5e does provide ways around that.
For example, there’s the awaken ooze spell (Dragon vol. 304), or the sentry ooze template (Dungeonscape), though the latter only provides “animal-like” Int 2. There are other templates that are not specific to oozes, but still legally applied to one, that provide more Intelligence. Ultimately, however, none of these rules officially make the cube playable.
Wizards used those same ideas in its own “Elite Opponents” article that includes a gelatinous cube monk, but it’s not playable either—monsters could take class levels in this edition. It gets around the gelatinous cube’s lack of Intelligence by using the fiendish creature template. They did similar things with other oozes in another “Elite Opponents” article.
There are also various oozes that are intelligent by default, mostly in Monster Manual II and III. These aren’t playable either.
(My answer to “Have oozes ever been a playable race?”)
So far as I can tell, those Elite Opponents articles are the only times Wizards of the Coast wrote up an intelligent ooze NPC for 3.5e.