'oboeru' is the normal way to say 'remember', like 'do you remember what he's called?'
'omoi dasu' is when something pops into your mind, like 'oh, now I remember!..'
or in the negative, it's like the memory won't come, like.. 'Oh.. I can't remember.. (but it will come to me later)'
That's my take, anyway. :)