This can be a problem when embedding an image file in another document, you have to rely on the application doing the processing to not do stuff you don't want. JPEG files are obviously of a format that the system can get away with reprocessing to reduce the amount of data. For an email service provider reducing data, both for storage and transmission, although pretty insignificant on an individual level is pretty immense when you consider total traffic. There is one simple way to ensure that your email provider doesn't mess with your images. Simply convert the image to a zip file. Although putting a JPEG file inside a zip file won't reduce the size of the data significantly, you might get a bit from compressing the text components and any attached colour profile, it will now be in a file format that the service provider cannot change without corrupting the file. Windows Explorer, or whatever they call it these days handles zip files pretty well now.
You have to be a little careful with services like Dropbox, since the link you send takes the viewer to a web page with a built in viewer system. While viewing the image in this system you are actually looking at a (usually) smaller sized preview with heavy compression etc. For the same data storage reasons, plus this also works on tablets and phones. If the person viewing the image simply does a right click save, they end up saving the preview, not the original image file. To get the original image you need to specifically use the download file option that Dropbox supply. I would expect Google Docs, and the similar Microsoft and Apple systems do much the same with image files.
I'm a Gmail user, and checking the settings for Gmail I see that they actually send images embedded in an email message, the sort that open automatically, via a proxy server, where they are transcoded. Whenever you see transcoding mentioned you may be sure that will result in the addition of extra levels of JPEG compression, and the stripping of any extraneous data, including attached colour profiles. I would expect most other services are much the same.