You've gotten some great answers :) -- I'd also add that it sounds like you have a major internal shift to make before it'll really work. You say that you feel bad and end up playing with them again right away...don't! Easier said than done, I know, especially if you enjoy playing with your kids, but it's critical for them to explore on their own. My 8-year-old also almost entirely lacks the capacity for independent play because his bio-dad and stepmom allow video games outside of school. If he's not in structured activities, he's twiddling his thumbs in front of a screen or playing with daycare kids. In contrast, my 2-year-old and 3-year-old can play by themselves just fine. They get about a half-hour of TV in the mornings, and maybe as much as an hour in the evenings. After that, they're either playing with toys that involve some form of imagination (i.e. Duplos, 8-year-old has Legos), reading books, or playing outside. I'll jump in and play soccer with them, or flop out on the floor and watch movies in the evenings, or randomly join in on the game every now and then, but otherwise give them the space to learn. My husband is a stay-at-home and I'm a work-at-home, so it's not easy to leave them alone to play sometimes. When we do, though, we see such huge differences in their development, and it's really clear how we're helping them by leaving them alone. It also seems to really help in forging a strong sibling bond.
I will note that these three are my husband's 5th, 6th and 7th kids. His other four were raised in a similar way. Today, the 19-year-old is in the army, while the three older ones are all college graduates, all very independent, and one travels the world. I have a whole bunch more I could say on the subject, so I may write a hub, but I'll just say that the biggest thing is to truly acknowledge that you're helping your kids by backing away. If it helps, think about this -- they're 15, 10, and 8 years away from being legal adults, at which time they're expected to know how to behave as independent adults. That's not much time, and our generation frequently waits until it's too late to start introducing adult expectations. Good luck! :)