Dropbox allows you to sync your files online and across your computers automatically. It provides up to 2Gb of storage for free and up to 100Gb for paid accounts. The iPhone app makes it easy to copy files from your computers or other mobile devices to your iPhone or iPad. For iOS or Android.
ToDo for iPhone and ToDo for iPad has a beautiful, simple interface and is full of features (projects, sub-tasks, due-dates, categories, etc), while remaining simple to use. ToDo makes it easy to keep your lists in sync between your mobile devices and computers. For iOS only. (Android users, try GTasks.)
Password manager for generating secure passwords and storing all you passwords securely. Synchronizes in the background with your computers and other mobile devices. A great way to avoid using the same password on every site. For iOS or Android.
Remotely access your Mac or Windows computers from anywhere. Control your desktop, move the mouse, zoom in and out via pinch-zoom. Very easy to set up and use compared to other similar programs. For iOS or Android.