Although online tools are still some way away from competing with a behemoth like Photoshop, PicMonkey is a dead simple online photo editor that can handle many kinds of complex edits in just a few clicks. You might even use it instead of Photoshop because it gets the job done so quickly.
PicMonkey is free and doesn't require a login, so you can just visit the site and drag an image into the drop zone to get started. It will upload and you'll see it on a big, wooden platform with a bunch of options to your left. You'll start out with basic touchups like colour, tone, brightness, contrast and other similar adjustments, and you can move on to frames and colour effects when you're ready. You can also fix skin blemishes, reduce red eye, remove wrinkles, put on a spray tan (weird!) and perform several other common touch-ups. Although PicMonkey is not a layer-based editor, you can overlay images and text.
Basically, if you're interested in performing common image-editing tasks in a snap from anywhere with an internet connection, PicMonkey will do the trick. One last thing to note -- sometimes the PicMonkey logo pops up on your image while you're editing but it doesn't seem to save it on the actual image. I'm not sure why it does this, but it doesn't seem to be anything to worry about.