I'm not actually talking about the morning glory flower but I thought I would just stick it there anyway since its a little more tasteful then having a picture featuring a tort stiffy and bed head there, but why do many men wake up in the morning with an erection although they might not necessarily actually be sexually aroused? 

Under more regular circumstances where erection is achieved through arousal there is a muscle that contracts on the urethra that stops urine from  being able to pass or at least makes it very difficult for it to. The urethra is the tube through which urine is expelled. Generally if you are still able to urinate whilst having an erection it tends to be a little painful and slow due to this muscle contraction on the urethra thats helping to obstruct its flow. At the point of orgasm sperm actually passes out from a different tube. So even from that biological point of view sex has very little to do with actual act of urination and its sensation. 

Need a little time to wake up... 
This in an extended way could have transferred as a mechanism to assist men from wetting themselves during sleep when they have a full bladder. This is why many men will wake up with an erection first thing in the morning despite not necessarily feeling sexually aroused. A slang term for this in English is "morning glory".