Is your budgie refusing to accept some freedom? If he prefers to stay in when you open his cage, don't despair. It could be fear or lack of confidence. It might take some time for your feathered friend to enjoy flying out to play.
Let your feathered friend come out when he feels like it. If you push him too hard, you'll end up with a freaked out bird who will never leave his cage. Close all windows and doors, shut the curtains -- so he doesn't crash against the glass when he does come out -- and just wait.
Make the room inviting. If you're playing hard rock at a deafening volume, do you really think your parakeet is going to come out? Turn very bright lights down, take the dog out and make sure the room is quiet. Curiosity will win out if the place doesn't sound and look terrifying.
Talk to him. Open the cage and sit close to it. Softly talk to your bird so he knows you're around and he won't be flying out into the unknown. If he trusts you, he'll be more likely to come say hi knowing you're there.
Bait him to come out. A nice plate of special seeds or fresh fruit would help. Place the food near the cage at first and move away, so you can observe without interrupting. Birdie will come out eventually to try out the yummy food. It could be for only a few seconds -- then back into the cage it is! Eventually, he'll realize being out of the cage is OK and venture out for longer periods of time. Move the plate away when that happens, to entice him to explore further.
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