You can definitely import raster images, for example JPEGs, to Adobe Illustrator as objects but that's not a proper conversion. Some other programs may offer saving to AI format, but most of them save the picture as object and do not convert bitmap data to vectors.
However, a lof of users are looking for a way to create a vector AI graphics from JPEG bitmap sources, for example to turn a picture of some logo to actual vector Illustrator graphics.
It's doable, but requires moderate knowledge of Illustrator and its functions, especially one called LiveTrace. This function basically allows bitmap to vector conversion, but requires that the person doing the tracing knows thing or two about the workflow in Illustrator.
You can find more about LiveTrace function in this excellent tutorial Converting Rasters to Vectors Using Live Trace in Illustrator by Mordy Golding.