There are a couple of cheap fountain pens on the market for around $3-$4 but in my experience there is only one good one and that is the Pilot Varsity (or V-Pen as it is know in other markets).
The Pilot Varsity is cheap disposable plastic-bodied fountain pen with a stainless steel nib. They come in seven colors and in only one nib grade: medium. [Edit: It has been brought to my attention that the Pilot “V-Pen” branded version is available with a fine nib (thank you Mark for the tip).]
The problem with most cheap fountain pens is a lack of quality control (and at $4 what do you expect?). Most of them work very poorly; the Platinum Preppy and Sailor Clear Candy immediately come to mind.
I have been using Varsity fountain pens for years now and I have only had one bad one. I have had closer to a 50% success rate with the Preppy.
The Varsity’s laser cut stainless steel nib is very smooth and quite springy. You can also write just as easily with the nib upside down. The medium point is on the finer side and should be agreeable to most users.
The ink is not waterproof and to my knowledge there is no way to refill a Varsity. Because of the rollerball-style feed you don’t have to worry (as much) about leaks or spills. These pens are as airplane friendly as your standard issue rollerball.
The body has a translucent grip section allowing you to see the feed and the body has a small ink view window.
The Varsity I photographed is the old pinstriped livery but everything else is the same on the current model.
The Varsity looks and feels inexpensive and as long as I can remember they have always been quite ugly. The new design is hideous as are the V-Pen branded models but they work well and that’s what counts.
If you want a cheap worry free fountain pen it’s hard to beat the Pilot Varsity.