My son is 14 and this problem has just started to get better. You're not alone -- that's why they still make pull-ups (disposable underwear)in larger sizes!
This is a hereditary thing. If there is anyone on either side of the family who has had this trouble, that's probably why your son does. Our doctor told us that when it's hereditary, you can do all kinds of stuff (urology work-ups, medicine,etc.) but basically you'll just have to wait until his bladder matures. This is more common in boys than girls, too.
We decided not to do the alarm system or drugs, and just wait it out until his bladder matured enough to let him know he needs to go. We put a vinyl-lined pad on the mattress and had him stop drinking after dinner and pee before getting into bed. In the last 4-6 months, we have finally started to see some consistency in his being dry in the morning.
CVS brand night time disposable underwear come in larger sizes, and do not have babyish looking pictures on them. When my son went to spend the night at someone's house, we just told him to wear them under his pj's and throw them away in a plastic grocery bag in the morning. He would just go straight to the bathroom with his clothes in the morning, change, and take care of his wet pull-up.
As they get bigger, and their bladders have a larger capacity, if they don't pee before they get into bed, sometimes the pull-up will leak.
When he was younger, I would sometimes tell the mother of the friend he was staying with what was going on, so she could remind them to go to the bathroom and then not make a big deal about his needing to throw out the wet pull-up quietly. As he got older, I let him handle it. Those pull-ups have worked for sleeping at home, friends' houses, and summer scout camp.
Mostly we worried about not having my son be embarrassed or feel bad about himself. We just kept talking to him about how everyone's body matures at a different rate, and this is how we were going to handle things until his bladder "grew up."
Hang in there. It does get better!