I always think I'll remember those details later, but brains are fickle things. Unless something jolts your memory, that idea will get blanketed by the weather and movies and that cute guy in your lit class.
Say you have an awesome dream: take out that notebook. Dreams allow you to experience things you don't actually experience, which is awesome for writing. My dreams are very vivid, so when a tsunami's coming to eat my town, I actually feel that terror. And when I'm a famous rockstar, I actually feel that fame. Your dreams let you into a world that has no limits and opens parts of your brain and imagination that you wouldn't have if you were awake. So, yeah, write that stuff down when you wake up and are lucid enough. Because that stuff is good.
I have tons and tons of story ideas written down - a lot of them I won't write a full book about, but I may incorporate it in another. Some take up all of my attention until I write a scene or two down. Some I look back on and think "REALLY?" But I know I will sit down with a lot of those ideas and write them out. And if I hadn't recorded them, they'd be lost in the crazy vortex that is my brain.
Even just writing how one moment feels, while you're sitting out in the sun and a hawk is flying in the sky and you're drinking lemonade out of your nephew's sippy cup because no other dishes are clean and life feels great. You probably won't experience that exact moment again, and sure - it's in your brain for nabbing - but only when your subconscious brings it up. If I wasn't writing this blog post, I wouldn't have brought up a scene like that, filed away in some part of my brain. But if I had written down exactly what it felt like, those memories and feelings would be fresh and I could pull from that at any time.
And I'm not saying record EVERYTHING, because you have to live. But if life hits you in the face or when you think about something from a different perspective or you see a beautiful, rusty gate or something, jot it down. Believe me, you'll be grateful later.