SendTo-Convert is an easy-to-use free tool which allows you to convert and resize images directly from Explorer.
Oddly, despite the entire point of the program being that it's available from Explorer's "Send To" menu, it won't add itself there by default. Either make sure you choose the "Add to Send To menu" option from the setup program, or launch Send-To Convert and check the "Add to..." box there.
Once configured, basic conversions are very straightforward. Select a few source images (JPEG, PNG, GIF, BMP, TIFF) in Explorer, right-click and choose Send To > SendTo-Convert, select a destination format (JPEG, PNG, GIF, BMP) and your images are converted immediately, and saved in the same folder as the source.
If you always use the same destination format then SendTo-Convert can be set up to use that automatically, saving a click as it won't need to prompt you.
There's good control over the destination folder. By default converted files are saved in the same location as the source, but they can also be output to subfolders, or a single custom folder of your choice.
In addition, there are a few file format setting (JPEG sampling and quality, an option to preserve transparency when converting between PNG and GIF). Send-To Convert also has a Resize option, but this is extremely simple, and can only shrink images while preserving their aspect ratio.