I own a Toyota. Both my parents own Toyotas. My fiancee owns a Toyota.
Why? Because they, like Honda, have a history of making good quality vehicles that, so long as one performs the specified maintenance at the proper intervals, essentially last as long as you'd care to own them. They certainly seem to have a corporate culture that promotes quality, though that may have been skimped on a bit in recent years. That will likely turn around after this whole thing blows over.
I've had friends who own different brands of cars, and some have done quite well, while others have had major mechanical problems even when taken care of regularly.
That said, everyone makes mistakes sometimes. Toyota's correcting those mistakes, and I have no qualms about buying another one. However, I likely won't have to for quite some time.
The one thing I wish is that they'd be more open, such as allowing the public to view "black box" information, provide codes and diagnostic information to the public, and provide more technical information in their manuals (Subaru has a lot of useful information, including listing different weight engine/gear oils based on climate, while Toyota only lists one weight.). Still, I suppose that's a business decision, and not something I can really fault them for...