These things, lots of people want to argue but the dumbest notions tend to be right.
Talking reliability, Toyota is king. Honda's close. JD Power's most reliable 2012 cars in each segment gave Toyota around 40% of slots. A car dealer did his own independent study this year and gave Toyota/Lexus the top two brands. Honda took slots 4 and 7 (GMC took 3, if you're wondering - I'll get back to that.) Here's a study done last year that looked at the cars most likely to hit 200k miles (this article excludes trucks and SUVs) and Toyota takes two of the slots (with Camry and Avalon). Honda took three of ten (with Accord at the #1 slot, Odyssey and Acura TL later on the list).
You can sift through all the studies in the world and you'll see, time and time again, Toyota and Honda come out on top. This stigma exists for a reason. Similarly, Land/Range Rover always scores low, Chrysler almost always seems below the other American automakers (and on the lower end in general).
The big issue with German cars is they're expensive. Regular maintenance costs a bit more with German cars, and that's what you'll find as more of the issue than repair costs. I'll warn you, I have nothing to back up this next statement with - I believe German cars need regular maintenance more, they need it to be reliable. As in, German car fans are more likely to go on with 'oh, yeah, it's every bit as reliable as an Asian car, you just need regular maintenance.' But if you stop giving a fuck, that reliability goes down, and it's not necessarily the same story for Toyota/Honda.
Europeans. I'd say avoid. Again, Land/Range Rovers consistently score low on reliability and Fiat can't build transmissions at the moment.
Jeep's Fiat-underpinned cars aren't reliable. The FCA 9-speed sucks. Did I go crazy on that point enough? This transmission also sits under the 200.
American cars - it's a crapshoot. In the big paragraph above on Toyota/Honda I mentioned I'd get back to GMC being #3 on a list of top ten reliable automakers, under Toyota/Lexus. I also linked cars most likely to make it past 200k and noted trucks and SUVs were excluded - from the list that included trucks,, eight of ten were Ford or GM, variants of the brand's pickup trucks and SUVs ("SUVs," here, meaning Expedition, Tahoe, Suburban and rebadges. In case you're wondering, the imports on the list were 4Runner (4) and Sequoia (9)).
So, again, GMC scored well - they make trucks ((I've heard their crossovers aren't the worst either, but that's another discussion). America does V8 trucks. Other vehicles - eh. You kind of have to go case by case. Generally, trucks aside, neither GM nor Ford is bulletproof, but they're not awful and not expensive. Who's on top at the moment probably depends on who you ask more than anything. Ford got a lot of shit for having bad infotainment systems (which affects reliability scores, because how do you judge how reliable a less-than-1-year-old-car is? Ask buyers if they've had issues. If they end up at the dealer frustrated with the radio, they've had issues).
Korean cars. Who knows.