3 Olives, I think you really need to quantify "inexpensive." Some people here see that word in reference to a camera and they think "less than $1." Others think "less than $100." A few think "less than $10,000." (OK, perhaps I exaggerate slightly on the range -- but not by much.) To give some examples in various ranges....
In the sub-$50 range, you'll find very little except for 35mm cameras. You might luck out with a low-end medium format TLR or folder, but most of these are a bit pricier than that. A few Holgas cost about $50; these are very low-end medium format cameras. (There are also 35mm Holgas, though, so be sure of what you're getting.) A used 110 or 126 camera could fit the description, but film will be hard to find -- 126 film was discontinued about a year ago, IIRC, although there may still be some in retail channels. I recently heard rumors that 110 film has ceased production, but I haven't seen that verified by reliable sources. Most 110 and 126 cameras are point-and-shoot models, so they won't produce great results, but they might be good if the teenager is interested in Lomography-style shooting, or if you happen to find one of the rarer "serious" models that used this format. In case you don't know, 110 film was a 16mm format that was popular in the 1970s for point-and-shoot cameras. The cameras and their negatives were tiny. 126 film was popular slightly earlier than 110 (in the late 1960s and early 1970s, roughly). It's the same size as 35mm film, but it's perforated and handled differently. 126 cameras produce square photos, which could be an interesting difference for a teenager who's experimenting with photography. (Many, but not all, medium format cameras also produce square photos.)
In the ~$100 range, various used MF TLRs and folders, as others have suggested, are options. Many of these lack built-in meters, so check for that, and factor in the cost of a meter if necessary. Another type of camera that might be of interest in this range is a 3D camera, such as a Stereo Realist. There are actually several types of these cameras. The one I'm most familiar with (the Realist; my father owned one) shoots 35mm slides, which are then viewed with a special viewer, which looks a bit like binoculars. These are mostly 35mm, but the format is unique enough that I think it deserves mention.
Going significantly beyond $100 (to $200-$1,000), options broaden considerably into high-end MF TLRs (the Mamiya C-series, for instance, although you might luck out and get a basic one for $100), MF SLRs, and so on. These are used prices, for the most part; few MF cameras sell for under $1,000 new, although a few do (Holgas, Kievs, maybe one or two others). You can get a pretty good camera in this range, although I suspect it's not what you mean by "inexpensive."