I'm in the same boat (10 years of experience, a good 6 doing serious programming work) with no degree.
However, because I know I will always do web programming I have definitely not focused on issues like compiler design, low level memory management [1], etc because most of the languages I use are either interpreted or compiled to bytecode and thus those areas are irrelevant
I would therefore argue it very much depends on what kind of work you wish to do - sure read some more in depth stuff but if you are doing web programming spending some of that time on product development knowledge, server administration, etc might be more beneficial.
[1] clearly some memory management is important in languages like Java and Objective C but using the built-in alloc/dealloc functionality is not really "low level understanding"
Just to follow up and explain... I'm at the end of my programming career (10 years, I've worked on high profile stuff, I'm done), having migrated away from programming into product development and strategy.
Programming may be completely different in a decade's time but I won't be programming. My era is now and that was always the plan to concentrate on web.
I fully respect the "career programmer" may need to choose differently but for many of us working as an engineer/programmer is simply a step in the journey. To go back to the OP, that's probably why I didn't feel inclined to study CS at university.
Oh. So, er, "I will always do web programming" actually meant "I'm not really going to be doing much of any sort of programming from now on". Fair enough, and that may well be a very wise career decision, but I don't think I can really be faulted for misunderstanding you.
However, because I know I will always do web programming I have definitely not focused on issues like compiler design, low level memory management [1], etc because most of the languages I use are either interpreted or compiled to bytecode and thus those areas are irrelevant
I would therefore argue it very much depends on what kind of work you wish to do - sure read some more in depth stuff but if you are doing web programming spending some of that time on product development knowledge, server administration, etc might be more beneficial.
[1] clearly some memory management is important in languages like Java and Objective C but using the built-in alloc/dealloc functionality is not really "low level understanding"