Not all of Valve's discarded ideas are great, the binned competitive multiplayer mode for Portal 2 is one such example, but some of them are. The video above is from a Valve talk at GDC in which they discussed many of the ideas that never made it into the full game. This scene was originally Portal 2's opening.
There were many more great ideas left on the drawing board. In fact, the whole game was set to pan out very differently. Eurogamer sat in on the conference, and describe out Wheatley was originally supposed to stay dead when Glados crushes him near the beginning. Rather than being a persistent companion, he was merely the first in a series of personality spheres you'd meet as you travelled through Aperture's labs. Other spheres included a paranoid AI and one that Valve's Eric Wolpaw calls "The Morgan Freeman sphere."
Players were originally supposed to find the Morgan Freeman sphere sat on a lonely stand in the middle of an empty room. "He'd been sitting on that little pedestal for a few centuries, and he was just incredibly, incredibly wise" said Wolpaw. "But only about the 20 by 20 space that he was in."
"As soon as you dragged him 22 feet out of the room, his mind was blown and he was pretty much useless. Although as the game progressed, he eventually got his feet under him and started delivering some homespun wisdom that all related back to this 20 by 20 space." Valve discarded the extra orbs when they found that players didn't bond to them as well as Wheatley, the first sphere went on to become an integral part of Portal 2's plot.
Valve were also planning to have several endings scattered throughout the campaign. "We had these parts throughout the game where Chell would die and that would be the end and we'd play a song, and if you wanted to you could just quit there." Wolpaw told the audience. "We had one that was like two minutes into the game, and if you died there, there was a song that was just about reviewing those first two minutes."
They also had a few other ideas. The next bit contains spoilers for the end of Portal 2 , in case you haven't played it yet.
Initially, there was a scene part way through the game in which you'd catch a glimpse of the moon. To trigger an early death you could portal up there to "asphyxiate while listening to a sad song about the moon." Valve eventually dropped the multiple endings because they felt as though they didn't have enough good ideas, but the moon went on to become Portal 2's memorable finale. According to Wolpaw, it was the "perfect mix of being totally awesome and completely stupid." It's hard to disagree.