Andy makes some good points. The real question, of course, is: how to prevent falling in the success trap - or how to get out of it if you've already fallen into it.
For me, the answer is: community. Especially if your boss is unwilling or unable to privide you with the opportunity to learn stuff outside your daily routine, you can learn an awful lot by immersing yourself in community.
This site is a great example. It offers articles, it has a forum where you can dive into questions asked by others and see if you can find the answer - or simply come back later and read the answers. It has a daily question, that often sets up a very interesting debate in the associated forum topic. You can learn a lot, just by participating here - but only if you make sure to put what you learn into practice!
Without practice, it will not stick. Go ahead and install SQL Server Developer Edition (or even Express, if you feel that $50 is too much to invest in future proofing your resume) on your home comoputer, then use some of your spare time every now and then to just play around with what you learn here. Copy that interesting query, execute it, check the execution plan. See if you can modify it to do something else. Try to set up database mirroring. Try a point in time restore on your play database, even if your day job does not involve backup and restore at all. Etc etc etc.
Of course, there are lots of other sites with great articles, quality bloggers, and/or lots of questions and answers. Just pick those you like and the number you have time for.
Another great place to be is SQL Server conferences. Not just the annual PASS Conference (though that is a great place to be); there are lots of other conferences as well, like e.g. SQL Rally, TechEd, virtual conferences like 24hrs of PASS. And if your boss refuses to give you time off and pay the conference entry fee, you can still attend a conference if you are willing to sacrifice a free saturday -there are SQLSaturday events being organised everywhere! And if you are at a conference, don't stick to attending topics in your comfort zone. If you're a dev, it still never hurts to attend a DBA session and learn about piecemeal restore - who knows if your next job requires that skill? Again, you can learn so many things from attending conferences- but (again) only if you make sure to put what you learn into practice!
Of course, official education, following courses, getting certification, all those help as well. But those almost always require cooperation from your company, in paying for the education and/or giving you time off to attend classes and sit exams. The nice thing about the community offerings is that you can do them (albeint in your spare time) even if your boss thinks that a DBA training for a BI specialist is a waste of money.
Hugo Kornelis, SQL Server MVP
Visit my SQL Server blog: http://sqlblog.com/blogs/hugo_kornelis