Allow me to chime in. First, regarding JPGs...they cannot contain Alpha Channels.....but they do contain four color channels!
Alpha JPG's (AJPG) are not normal RGB+A Images like TGA's, they are CMYK Images. Moving along, James is correct, PNG is the way to go. They have alpha channels (variable transparency), gamma correction (cross-platform control of image brightness), and two-dimensional interlacing (a method of progressive display). For image editing, either professional or otherwise, PNG provides a useful format for the storage of intermediate stages of editing. Since PNG's compression is fully lossless--and since it supports up to 48-bit truecolor or 16-bit grayscale--saving, restoring and re-saving an image will not degrade its quality, unlike standard JPEG (even at its highest quality settings). And unlike TIFF, the PNG specification leaves no room for implementors to pick and choose what features they'll support; the result is that a PNG image saved in one app is readable in any other PNG-supporting application. Like GIF and TIFF, PNG is a raster format, which is to say, it represents an image as a two-dimensional array of colored dots (pixels).
...and I am veering off topic. I apologize. So I took the image you posted that had the unwanted white background and loaded it into Photoshop. For reasons of available time, I just used the magic wand to select (and then delete) the white background. Then, instead of just using the Save feature, I used the Save for Web
functionality and chose PNG format. If you just use the Save functionality, it will not preserve the transparency. After that, I just launched FrameForge and applied that blood.png as a decal to some flooring and voila
....blood splatter. Admittedly, its not my best graphics work but for the sake of time, it will do for this demonstration. The graphic with the alpha channel is attached. Enjoy.