In some cases you need to compress image without compromise image quality, for example when the target is the web publishing, or if they must be embedded in documentation or slides, or in email attachments, etc…
There are various online services for this purpose, they easily allow to compress images in various formats preserving quality (lossless compression).
Compressor.io support 4 different formats: JPEG, PNG, GIF, SVG.
Kraken.io the basic web interface is free with some limits (eg. 1mb max file size, images are available for download for 12 hours) the PRO offer more features (URL Paster and Page Cruncher, image resizing).
TinyPNG support .PNG (also transparent) and .JPG formats (up to 20 images, max 5mb each), there is also a paid Photoshop plugin available.
Compress.photos compress .PNG and .JPG images.
Optimizilla allows to compress JPEG and PNG images.
There are also free software for image compression:
FILEminimizer pictures for Windows. Support various formats (JPG, BMP, GIF, TIFF, PNG and EMF), support batch process. In the program settings you can set the flag for lossless output.
FileOptimizer is an advanced file optimizer for Windows, support many formats and use different compression engines (they are listed in the page).
ImageOptim for Mac OS X, multilanguage.
CaesiumPH JPEG lossless compression, for Windows and Mac OS X.
Trimage graphic interface and command line, there are packages available for various Linux distributions.
RIOT permette di ottimizzare immagini JPEG, GIF e PNG, supporta plugins per IrfanView, GIMP, XnView.
Pingo is an experimental PNG/JPG optimizer for Windows with visually lossless or lossy compression.