I'm playing a career mode game, and I've gotten my research up to all of level 4, plus Electrics. I've flown a number of suborbital hops, plus one successful orbital flight with re-entry.
The Mk1 Command Pod by itself is nicely self-stabilizing during re-entry: make sure it enters the atmosphere blunt-end first, and aerodynamics take care of the rest.
For suborbital tourist flights, I'm using a command pod stacked on top of a Mk1 Crew Cabin on top of a heat shield. This is "stable" in the sense that I've never had one flip over and go pointy-end first, but it requires active flying during re-entry to keep that from happening. I can't see this being viable for orbital tourist flights.
My first attempt at orbital re-entry had a command pod stacked on top of a 1.25m Service Bay with a few experiments on top of a heat shield. This quickly tumbled during re-entry, with predictably exciting results.
Is it possible for me to make a stable re-entry vehicle more sophisticated than a simple command pod with heat shield?