Most wordpress themes are now 'responsive'. They have to. But most site owners don't have a clue. They now know & generally agree that there should be a 'mobile' version for their website. And with 'responsive' being the new catch phrase, if a theme is said to be 'responsive' they accept it.
Themes were rarely used as it is, particularly if it's used in a business website. So customization is the order of the day. Site owners still see their website as a brochure or paper design. They often come up with a requiment like this, '... this button should appear above the fold'.
If you feel there is nothing wrong in above requirement, please search for 'is there a fold' on the internet, or see here on why there is no page fold on the website.(Yes, these were created by very frustrated web designer / developer)
We must decide on how the website should appear on various screen sizes before attempting to customize a responsive theme.
If you are a site owner who understands the value of keeping your site 'responsive'. here are the list of themes I felt comfortable to customize.
There are quite a lot of other responsive themes which seems promsing for customization. I haven't personally used them though.