Okay, let me limber up my fingers here before I begin.
I must apologize in advance if my tone is a bit testy, but I just spent two days in court on the most ridiculous thing you can imagine, and I'm a little edgy. So don't mind me.
First, does your neighbor have any other means of ingress and egress from his property? If not, then he has always possessed an easement for purposes of getting in and out of his property--this would show on your title search, assuming you had one done. It's very common in landlocked situations, where people subdivided a larger parcel front-to-back, rather than side-by-side--you see it a lot where siblings divide up the family farm after the folks die, and now we're a couple generations down the road, no one related owns all the separate parcels and the fight is on. That having been said, it doesn't mean he can BUILD on the easement! It just means he can walk, drive, run his horse and buggy down it.
Second, and this is VERY IMPORTANT, how LONG has he been doing this? If he is using your property in an "open and notorious" fashion (ain't law grand?), he can "tack" on the time he was doing it with prior owners to the time he's doing it now, to make out an "adverse possession" claim. Generally speaking, that requires a 20-year period of use, but some jurisdictions do vary, and since I don't know where you live, I can't say for sure. At any rate, it is very important that you nip this in the bud, as they say.
The VERY FIRST THING to do is to have a survey done, if you don't already have one, and determine PRECISELY what portion of your property he is squatting on.
The VERY NEXT THING to do, WITHOUT DELAY, is send him a letter by certified mail, keeping a copy in your safe deposit box, demanding that he keep his paws and his sheds off your property, and giving him a deadline by which the sheds must be moved, or you will be forced to consult with an attorney, to much unnecessary expense and unneighborliness to you both, blah, blah, blah. If your driveway is NOT his only means of ingress and egress from his property, you should also inform him he is no longer welcome to use this path, and that any future use will be considered trespass. Your letter should of course be simple, to the point, and contain no swear words. You don't want to inflame the interloper unnecessarily.
It is unfortunate that the tone of your letter is required to be rather forceful, however, the law requires in such matters that the "rightful owner" "affirmatively assert his rights" to the "sole use and enjoyment" of his property. While you certainly can begin by trying to have a nice, neighborly conversation about "gee, it sure would be nice if you weren't taking over my driveway," etc., if you leave it at this with no follow-up with a letter such as I've suggested, this may unfortunately be seen in court--where I suspect you will eventually find yourself--as acquiescence to his use of your property.
The VERY NEXT THING after that, is to take a second copy of your letter to a lawyer who HAS EXPERIENCE IN LAND USE LAW and ZONING. Do not automatically assume that someone who does real estate closings has land use/zoning experience. ASK. Ask how many cases they've handled; ask about the fact situations; ask about the outcomes. It is my experience that this is an area of law that a lot of attorneys either think they know a lot about or think its easy, until they end up in 6 years worth of appeals because they were WRONG.
Please feel free to post back with any additional information or questions. I'll do my best to answer.