Most regen receiver circuits use the coil as part of the path to provide positive feedback that is required to deliver the high gain that this configuration is famous for. And to allow reception of SSB and CW signals. This is either done by tapping the coil (often the source in a FET design is connected to the coil tap) or with a second, smaller winding. One side of this usually goes to the drain (if a FET design) or collector (if a BJT design).
However, just like VFO circuits it's possible to not have a tapped coil and use capacitors instead. Such as with this Tandy/Radioshack receiver kit. Also see here for the instructions (it's a 3 transistor shortwave regen).
I knocked one up and got it to oscillate. Not only that but I could hear amateur SSB signals on 7 MHz. It wasn't stable but this was due to my open-air test design with no shielding. Anyway if you're after a simple regen I suggest you try this type. My coil was about 20 or 30 turns over a T50-2 toroid. And the variable capacitor? Approx 10 - 200pF.
My unit just has a single transistor detector directly driving a TL431 (discussed yesterday). That has enough gain to directly drive a speaker on ham signals. If you build one please let me know your experiences in the comments below.
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