The AF Opus X is an obvious choice. Anyone who smokes cigars should try one at least once in their lives.
Ashton is a solid brand. If they have it, I recommend the Cabinet.
CAO is a solid brand, but I'd avoid their global series (Americana, Brasilia, Italiana). I'd stick to the 'X2s' (CX2, LX2, and MX2).
Cohiba is a very solid brand. I recommend just about anything from them. Never had a bad experience with anything, though if you've got a light stomach or haven't eaten much, I'd steer clear of their maduros. They'll kick you in the teeth.
I think Diamond Crown is a very underrated cigar brand. Doesn't get the accolades that the older companies with Latin-sounding names do, but if you can find the Diamond Crown Maximus, I think it's important you try it.
H Upman is one I hadn't tried until recently, but it's a solid brand. I've only had two, but both were good quality cigars.
I've heard good things like Hoyo de Monterrey, but I've never gotten around to trying them.
Macanudo is a quality brand, but the Jade (light green wrapper) is uninteresting. However, if you see a Macanudo 1968 (I see it on there) or the Vintage Maduro 1997, get them. If the 1968 comes in a "Gigante" size, I recommend that one.
Monte Cristo is a high-quality brand ... I'd put it in the same camp as Cohiba.
Oliva is a decent brand, but I'd stick to Series M and Series O. If you're feeling bold, go with the Series V, as it's a very unique cigar ... the smoke has a green tint to it, but the level of nicotine is pretty high, so if you're not ready for it, you'll have a green tint as well. A friend of mine threw up when I gave him one.
Punch is a solid brand. If you can find the Punch Champion, I specifically recommend that one.
There are others on there that are okay, but those are the ones I'd recommend.