Needless to say it is better to keep your pictures and illustrations in vectors today, because they are more and more supported by browsers as well as other applications and they can be quickly converted to raster at anytime. However, the reverse process is not straightforward.
There are plenty of JPG / PNG / BMP to SVG convertors around the internet. You can see the best of them in the list on right side. Nevertheless, the professional ones are paid and free ones have many issues. Moreover, even if you use an oustanding conversion tool, it wouldn't be without difficulties.
Because during this procces geometric data has
to be reconstructed from the raster. In other words, points, edges
and curves have to be found in the array of pixels; that leads to
image recognition and edge detection. But even if some software
reconstructs the shapes in picture, the hardest task is still needed
to be done...
Gradients, blurs etc. have to be applied in order to match the original picture. And that is the real challenge for conversion tools.
Even if you had a super tool that performed all above mentioned taks and produced SVG with perfect quality, then there would always remain one important thing; and that is optimality. Vectorized pictures consume both your cpu and your memory. Why and how? Because algorithms always try to approximate curves, gradients etc, but finally they would end up with more elements than original author needed to. These elements stored in SVG format consume more memory and because all of them have to be passed through rasterization process everytime picure is rendered, they consume also more CPU time.
Instead of vectorizing a raster image, it is better to find a free vector that suits you the most.
Simple, fast, free and without adds. Limit for image is 1 MB. Supports SVG, PDF, EPS, DXF, XFIG.
Simple and fast with limit of 5 MB. Adds are present. Supports SVG, PDF, EPS, PS, DXF.
Simple fast, allows uploading larger images, however annoys with popup adds. Supports SVG, PDF, EPS, DXF, AI.
Quality BW vectors, many settings, Dropbox and Goole drive integration. But not very intuitive and with adds.
Simple and fast, but maximum 100 KB is allowed, captcha is required, many annoying adds are present.