iPhone/iPod touch: Simplenote launched as a $US3, then $US2 app that filled a huge gap in the iPhone's connectivity — a note-taking app that synchronises. Now it's a free, ad-supported app, so there's no reason not to grab it.
Simplenote itself is nothing too fancy, but it does get the job done. You create notes, write them in Helvetica as opposed to the default Notes app's marker-style font, and can type in portrait or landscape modes. The app saves as you go along, and you can search out text in your notes right from the home screen.
When you start up Simplenote, you'll be asked to create an online account to sync to, and you obviously should. The web interface is clean, offers in-note search, and you can edit your notes from there and sync them back again to your devices.
In its current free form, Simplenote puts fairly unobtrusive ads at the top of your main menu and note writing screens. They're not the worst ads you've seen, mainly tacked to software and other apps, and it seems like you won't get hit up with One Weird Old Tip to Weight Loss. If you pay $US4.99 per year for Premium services, or previously paid the $US3 or $US2 price, the ads go away, and you get a lot of other nice features, like an RSS feed of notes, per-version backup, and adding notes by email.
Simplenote is a free download for iPhones and iPod touch models running at least the 3.0 software. If you've got another solution you prefer for synchronised, easy note taking on the iPhone — besides maybe Evernote, which is its own, much larger-scale solution — tell us about it in the comments.