Can cactus grow in the nether or the end?

Nothing is said against it. Plus, from what I've seen in various let's play, cactus seems to grow with no problem in the end.

P.S. (Studoku reply) If you are really trying to prickle the Ender Dragon, at least get it on video. =D

Yes, you can grow basically every crop in the end. All plant types and all crops will grow normally, but they will grow significantly slower, due to the lack of any light source. You can counteract this effect with two options

1. Light up the area. Besides making crops grow faster, this will also prevent more endermen from spawning as often.
2. Bonemeal the plants. This isn't the recommended option, as it will take quite a lot of bonemeal for the plants to grow.

Source: I have done this many times myself in both the Nether and the End, and the Minecraft Survial Series explains it as well in more detail.