How can I tell if a rental aircraft has been maintained in good condition?
From a fatigue perspective, this isn't really that much of a concern.  The beauty of metal structures is if they get &quot;overloaded&quot; one time, but the overload was not past the permanent deformation point, the yield point, of the affected structure so that nothing is permanently bent, the structure is fine, in general.  A hard landing that did hidden damage to the gear box should get detected at the next annual.
If you do a careful walk around and include gentle pokes and prods with your inspection, looking for loose bits or sloppy clearances, and everything is reasonably tight and straight, the chances of the thing letting go on you for no reason, while you are minding your own business sightseeing, are microscopic.  Look for stories of 172s just falling out of the sky because the wings let go without warning, and you will be looking for a long time.
Cessna once tracked down, back in the 70s, the most beat up high time 172 they could find, and located a 12000 hour airframe that had been used for pipeline patrol, to see how it was holding up.  It just required replacement of hinge bearings IIRC.  Corrosion is the bigger concern than overloads, and I might be wary of a 172 that has spent its entire life tied down outside (it's the daily condensation cycles that's the killer for outside parking unless it's in the desert) unless I was confident that the maintenance at the operation was good.  A 172 that is hangered every night will pretty much go forever.
Same with engines. Lycs and Conts are built like air cooled tractor engines.  Slow turning with large clearances and thick, heavy cranks and connecting rods, dual ignition, simple carburetors.  They usually give off warning signs if they are going to blow up on you (for example, an impending main bearing failure typically results in major amounts of oil coming out the breather line and coating the belly as the excess oil spews out the bearing and fills the crankcase with spray). When Lycomings go bad it's usually their weak point, the camshaft lobes, going south, and this puts metal shavings in the oil filter long before engine operation is affected, which should get caught at annual (as the cam lobe wears down eventually the engine will lose power and misfire).
If it starts nicely, runs nicely making normal static RPM at full power, oil pressure comes up smartly, isn't dumping oil everywhere, no crazy vibrations or scary sounds, the chances of the thing blowing up on you are maybe not microscopic, but pretty small.  Be observant of the FBO's maintenance operation; organization, cleanliness etc.
Learn some of the warning signs of engine trouble (like &quot;morning sickness&quot;; rough running that goes away as the engine warms up, a sure sign of a sticking exhaust valve, and which is guaranteed to get worse).
Statistically speaking, if you are flying around in a halfway decently maintained, straight and tight 172, at 3000 ft on a nice day, with gas and oil in the thing, you really have to work at it to kill yourself.