aleep 指睡着，只用作表语或者补足语。

eg.He was fast asleep.I couldn't wake him. 他睡得很熟，我叫不醒他。

   He is sound asleep. 他酣睡着。

   I found him asleep. 我发现他睡着了。

go to bed（北京家教中心www.beishidajiajiao.com）

go to bed 指就寝，不一定睡着。

eg. I didn't go to bed until eleven o'clock last night. 昨晚我十一点才上床睡觉。

    You should go to bed now. 你该上床了。

    Don't disturb her;she's gone to bed. 她上床了，别打扰她。

sleep 

sleep 指睡眠

eg. He likes to sleep for an hour in the afternoon. 他喜欢午后睡一个小时。

    I didn't sleep well last night. 我昨晚没睡好。 

    He sleeps late. 他爱睡懒觉。

sleeping 与asleep 同义，但可以作定语。

eg. The sleeping child is her son. 这个睡着的孩子是她的儿子。

    A sleeping man lay on the pubic road. 一个睡着的男人躺在大路上。

sleepy

sleepy 指困倦欲睡，但并没有睡着。 

eg. I felt sleepy. 我很想睡了。

    The child was so sleepy that his head was nodding. 那孩子很困，直打瞌睡。