I had to fly internationally a lot for my work, at one point I was flying close to 300,000 miles per year. Anyways, my favorite two international airliners are British Airways and Singapore Airlines. But I have also flown a number of times on Emirates and Qatar airways and those are really nice too - except for the fact that you're flying with a ton of Arabs - so that gets annoying (Yes I am Arab and I hate other Arabs lol).
I was a Gold card with British Airways and you really got a lot of perks with them, the lounges in Heathrow were nice (although not as nice as Singapore Airline's lounge in Singapore), fast track through security check points, always guaranteed a seat on any British Airways flight even if its fully booked, priority check in, etc. But their gold card is one of the hardest to maintain in comparison to other airliners, you really have to put in a lot of time in the air with them.
Domestically in the US I love Virgin and I love Jet Blue. Really can't go wrong with either one of those, even if you have to pay a little more.
Worst airlines I've ever been on: Iberia - FUCKING AWFUL! And I've flown with them a number of times from Madrid to South America (12-14 hour flights one shot) and it was really really really bad! Another REALLY bad airlines - Egypt Air! Shitty ass service! Oh and I hate Southwest... although they are cheap and almost always on time.... but old ass planes and basic service!
Edit: Add to the list of worst airliners I've been on - China Air (though the food was actually good) and Dragon Air..... ugh!