CCD and CMOS imaging devices consist of grids of light sensitive cells, so they intrinsically generate pixel based data(old chemical film isn't strictly pixelated in the same sense, since its light sensitive elements aren't arranged in a grid; but it has "grain" which is a function of the size of its light sensitive regions, which is somewhat similar. It tends to be less of an issue; because we have over 100 years experience with making very fine grained film cheaply and substantially less with making high resolution sensors cheaply).
It is perfectly possible to "trace" manually or algorithmically, a bitmap image to produce a vector image(inkscape is free and has a tool for doing so, if you want to play around, I think adobe has the high powered product in the area); but doing so generally means throwing away substantial amounts of detail or ending up with a vector description so complex that it is larger than a bitmap of the same image. Vectors are absolutely superb for situations like fonts and icons, where substantial color and detail are not necessary; but you don't want gross pixelated edges if you zoom.
While I'm rambling, I ran into one case a while back where converting a bitmap to vector absolutely saved the day. I was working for a school IT department, and the Vice Principal comes in, with an 8.5x11 sheet, probably a photocopy of a photocopy of a photocopy, of the school's floorplan. He says "Can you blow this up, I want to print large floorplan posters for Parent Teacher Conference Night." I tell him that I'll see what I can do. I scan it, and it already looks pretty lousy. Lots of specks and stuff. As a test, I resize it from 8.5x11 to the 3.5 foot poster size he wants. Absolutely dreadful, pixel hell, completely unusable. I download inkscape and fiddle with the bitmap trace tool for a while, and get a vector that captures most of the intended detail, without too many of the specks. It resizes beautifully. The trace wasn't perfect, a lot of what should be straight lines have slight curves on their edges caused by photocopy smudge, but slight curves look way less annoying than gigantic blocky pixels when you are trying to read a poster from a few feet away. The floor plan should have been preserved as a vector image in the first place, and the excursion into bitmap land and analog copy world did it no good; but, for images that are largely "vectorish" anyway, bitmap tracing can do a fairly good job of saving the day. For curiosity's sake, I tested a bunch of ordinary pictures when I was playing with inkscape, and the results weren't nearly as good. The effect was kind of cool, I can definitely imagine instances were it would be artistically desirable; but the loss of detail was massive, unless you produced a vector file 10s to hundreds of times larger than the bitmap.