See Starise, how Bubba's words of reassurance are very comforting........ 

Rats
or 
mice
or 
poltergeist
or
Occam's Razor
 
You decide
 

Get electrical contact cleaner and spray it in there, or take apart the doorbell and bend the contact so you have to push it in a little more to make it contact, and all the cleaning stuff for moisture and things that can be done to equipment like that they make in spray type cans whatever or lube type stuff.
 

It was me.  Sorry.  I used a large pogo stick to hop up on your roof.  I'm surprised you didn't hear me landing up there.  

Could it be the NSA - or NASA?
Perhaps a drone strike?
After all, one crashed in Iran a few years ago, so they can go 'rogue'.
 
When I was about 10-11, my best friend & I would ring the door bell at a house a few blocks away. It was a house that was 3 doors away from a traffic light, which we could see from there, so we'd wait & time the light, ring the bell & then run like hell.
So maybe it's a re-visit from me [& the ghost from my childhood past] being reminded of something I now need to fess up to & apologize for - you know - while I still can. 

*Ding dong!*
(Runs away and hides while snickering.)

Ok Star...this has been going on for quite some time now.
I'm thinking your trouble-shooting skills aren't cutting it and maybe it's
time to call for backup....especially after reading Bubba's post.

Spacey- I guess other than looking for mice and at the wire . I have done all I can do at this point.
 
I am a troubleshooter by trade. The most difficult kinds of problems to eliminate can be the intermittent ones. If this isn't intermittent nothing is. In my experience with 99% of all intermittent problems both electronic and mechanical the problem usually gets progressively worse with time. According to that logic the bell will either go out completely or the rings will become more frequent. In the last 6 months neither of those has happened. I haven't ruled out a mouse who decides to munch very occasionally at the same place, but even if that's the case, then we have the makings of an eventual short circuit.Humidity and temperature doesn't seem to make any difference.
 
According to my thinking the way a button system works is that there is tension on the spring mechanism keeping the contacts open until someone pushes it. If there was a problem with the button itself ,  say with the spring tension....then the button would stay on the contact and the bell would be going crazy which it hasn't. The spring would get progressivly weaker and eventually the bell would be ringing constantly or not at all.
 
The "ghost" part of this is yet another possibility but it leaves far more questions than answers. How can something that is in a spirit form interact with something that is in the physical realm and why would it? I believe that in other cases it either happens or fools an observer into thinking it's happening.In this case I can't say. Most paranormal "trickster" type  activity gets worse over time in cases of haunted houses. I haven't seen this get worse yet.
 
Too much I don't know  about the why. I ask questions like, If this thing has the ability to pass through physical material i.e. walls, then why would it ring a bell? Possible answer- So you know it's there. If this is true , then the next set of questions are, Why would it want you to know it's there? And what is it?  If it has the ability to influence physical matter, then it could theoretically do other things with that same ability...I'll leave it at this. I believe in the other side, but I don't have a clue how it operates and If I don't know that I can't go very much further.
 
If it's Craigb or Old55 or Jimusic, I'll catch up to you 
 
 
 
 

Ok, here's another take on this.
 
Does anyone else hear the doorbell, or is it just you? If your wife hears it, does she just say that she hears it to wind you up or does she really hear it?
 
Do the bells tell you to do bad things?