There is no one answer to this question. Some premium themes offer very good value for your money while others are hardly worth downloading if they were free. It is important to understand that far from all premium themes are good themes and you need to carefully choose which theme you want to buy if you are going to buy a premium theme.
With that being said we should get back to the question at hand. Is it worth paying a premium theme? The answer to this question depends on who you are and why you are looking for a theme
Beginner building your first website
If you are a beginner that is building your first website then I do not think it is worth paying for a premium theme. At least not at first. You still have a lot to learn and it is going to be very hard for you to make an informed decision about which theme you should choose. I recommend that you save your money and use a free theme instead of buying a premium theme. This way you can get started without having to spend more money then you need to. Your website will hopefully grow and once you are 6 to 12 months down the line you can upgrade to a premium theme if you feel that your website needs one. At this point you will know exactly what you need from the theme you buy as you will have experience running a website.
Experienced webpage builder
You will know better than me whether the project your are working on needs a premium theme. It is usually worth to invest the money necessary to build the website you envision right from the start. This includes paying for a premium theme if your think that is going to make your website better.
Beginner building small scale commercial website
If you are trying to start a commercial website in the hope of making money on a limited budget then you should definitely be paying for a premium theme. They are in this situation more than worth their cost. A premium theme will give you a more professional looking website than a free theme would and there is less chance that your visitors have seen other websites with the same design. A premium theme is a great way to get a professional website without spending too much money.
Large commercial venture
If you are working on a larger commercial venture then you should never buy a premium theme. They offer good value for money but are sold to a large number of different websites. A commercial venture of this type should always use a custom developed designed that is unique to their website. Having a custom design help develop trust. Trust that will convert into more business. If you use a premium or free theme then your business will feel less professional and less trustworthy. Any project with a budget of more than USD 25 000 should have a custom design. Projects over 10 000 should consider using a custom design.