I get asked a lot what image editors are useful, intuitive and free.
When I’m without an Internet connection, I use Pixelmator on my Mac. It’s not free, but it is a good tool for a reasonable price.
For things like cropping and resizing, many of our online services have built-in editors. But for more advanced options, and better overall control (think homepage images for websites, headers for newsletters, etc.) you might just fall in love with PIXLR (linked above).