Depending on whether the mail client supports it, you could in theory use the data URI scheme, like so:
<img src="data:image/png;base64,
iVBORw0KGgoAAAANSUhEUgAAAAoAAAAKCAYAAACNMs+9AAAABGdBTUEAALGP
C/xhBQAAAAlwSFlzAAALEwAACxMBAJqcGAAAAAd0SU1FB9YGARc5KB0XV+IA
AAAddEVYdENvbW1lbnQAQ3JlYXRlZCB3aXRoIFRoZSBHSU1Q72QlbgAAAF1J
REFUGNO9zL0NglAAxPEfdLTs4BZM4DIO4C7OwQg2JoQ9LE1exdlYvBBeZ7jq
ch9//q1uH4TLzw4d6+ErXMMcXuHWxId3KOETnnXXV6MJpcq2MLaI97CER3N0
vr4MkhoXe0rZigAAAABJRU5ErkJggg==" alt="Red dot" />
Again, the support is mail client dependent. Some might not support it at all. Some might truncate after a X amount of bytes. Etcetera. As far as I know there aren't many of them. Further I don't see another ways to inline images in HTML like that. Until the support is widespread, your best bet is really to send the images along as an attachment.
Update as per the OP's update: well, most of the modern webbrowsers supports it. The aforementioned Wikipedia link even mentions them in detail.
Data URIs are currently supported by the following web browsers:
- Gecko-based, such as Firefox, XeroBank, Camino, Fennec and K-Meleon
- Konqueror, via KDE's KIO slaves input/output system
- Opera (including devices such as the Nintendo DSi or Wii)
- WebKit-based, such as Safari (including on iPhones), Android's browser, Epiphany and Midori (WebKit is a derivative of Konqueror's KHTML engine, but Mac OS X does not share the KIO architecture so the implementations are different), as well as Webkit/Chromium-based, such as Chrome and Iron
- Internet Explorer 8: Microsoft has limited its support to certain "non-navigable" content for security reasons, including concerns that JavaScript embedded in a data URI may not be interpretable by script filters such as those used by web-based email clients. Data URIs must be smaller than 32 KiB.
Note that IE8 truncates the string after 32KB. So, as long as the images aren't that large, you could use the data URI scheme for IE8 users. It's not supported on IE7 and lower.