You can achieve a luxury/expensive/premium aesthetic with some of the following treatments

• Dark background colours
• A single highlight colour: gold, purple or yellow.
• Thin subtle understated illustrative patterns
• High quality typefaces and fine typography, sans or serif, keep it thin though, perhaps use details like ligatures.
• High quality photography of luxurious environments and wealthy looking people.
• Smart, relaxed, confident tone of voice, don't do any hard selling.

If you haven't already, take a look at Uber's brand guide, they achieve this look pretty well. http://brand.uber.com/#menu

I've thought about this a lot too, awesome to see this being discussed here.

From what I've determined: Premium need lots of negative space. Copy should never feel overly large or chunky. Premium certainly doesn't yell. Color should be restrained, and if used it should not be obnoxiously bright. As others have said, thin type is also key. Things should look heavily ordered and aligned to a strong grid-based structure.

Less is more is the golden rule. Don't say too much, it should feel like an exclusive club where people don't really need a lot of detail, its more about the general vibe. The content should live within an excessive amount of space with minimal content, as if to imply that a small amount of detail is so valuable that it deserves a large amount of space to exist. A small, crowded room is not luxurious; spacious and wide open is what a lot of money can afford.

Adding to what has already been said:

• Consistency: high-end brands are consistent, consistent, consistent. Everything matches; everything uses the same colour (Hermès orange), has the same pattern (Louis Vuitton), or is sold in the same packaging (Chanel No5). This consistency communicates heritage and longevity. Luxury products aren't created overnight, but are the result of cumulative years of craft, precision, and experience.

• Understated confidence: like Bevan said, luxury brands don't sell hard because they don't need to. Their reputation and cultural weight means that the products sell themselves. A confident, understated presentation of the product without over-explaining is are an example of this restraint.

• Ignoring trends: basically as a result of consistency and understated confidence, luxury brands don't change their image or approach with the latest trends. This makes them sometimes seem out of touch, but also means they stand out from the crowd.

Thanks for the replies, these are really good. The main principles I'm pulling so far are:

• don't be a try-hard, be confident and understated
• indications of scarcity and focus (gold, thin typefaces, lots of whitespace)

I'll amend or post again if other comments come in.

Gold/black/white colour schemes.

Clean thin san-serif fonts or serif font with very little flourish.

These two design choices can make a design (UI/graphics/packaging etc) look premium.