I was looking for an app for my IPhone 4 that would sync with my MBP automatically. Found Evernote. Free app. Download to MBP and IPhone. I can write notes on my MBP and it syncs automatically with my IPhone and vice versa. You can have different notebooks, for different reminders. Nice.
It does everything you said it does, and it does it very well. I use it for some things.
However, for large projects (I am talking here about research, school, and work projects), Evernote is really quite awful in three respects.
First, it is really tough to organize things. You can (finally) make notebooks and sub-notebooks. This is helpful. It is not especially great if you want to have one note participate in two notebooks. Yes, I know there are tags, but those are pretty clunky.
Second, you cannot link conveniently to different notes (there is a workaround, but it is clunky). The developers are well aware of the desire among a lot of users for features like this, but they refuse to consider putting them into the program.
Third, it doesn't play well with your files. Upload limits are low for the free account and you cannot link to files in your drive.
I recommend giving a program like VoodooPad a try. The syncing is not nearly as robust as Evernote (really, Evernote is one of the most incredible pieces of software out there in this respect), but it works. Best of all, organization is very flexible and linking is simple.
Obviously, the big difference is that VoodooPad does not live on the web, so it isn't as accessible. Use it with an online backup service like Sugarsync, though, and you are pretty close in terms of functionality.