I have recently come into the possesion of a used Delorian of unique capabilities. Unfortunetly, despite its many after-market additions and modifications, it still requires gasoline to make it run. 
This may prove a problem because of the fmany, “out of the way” voyages I have planned. So, how far back could I go and still get gas for my car? Regular or diesel? Leaded or unleaded?
The answer is really going to depend on the precise engine of your vehicle.
Many diesel engines have high tolerances for fuel and will run indefinitely (if not entirely happily) on olive oil or other vegetable oils with some simple modification like heating elements to keep it liquefied. In that respect you could have obtained fuel easily at least 300 years back and could probably have manufactured oil any time in the last few million years.
In contrast if your vehicle runs properly only on premium leaded gasoline you may not be able to get fuel for it today on some parts of the world.
Basically we need more info. Whatis the exact engine, and how far are you allowed to travel geographically when you’ve finished time travelling for example. If you drop down in Venezuela in 1920 you would probably have trouble getting any fuel at all, but if you can fly up to the US you could get it fairly readily.
What Blake said, although as far as petrol/gasoline engines go, you could obtain “motoring spirit” at some pharmacies and drug stores from about 1900-1910, IIRC. I believe this stuff was unleaded, which is good, but it might have problems with octane for the modern engine. It’d no doubt get you home.
The Duryea brothers built their first cars in the US in 1896, which leads me to believe that gasolene must have been available around then. It would have been a low-octane, unleaded variety, which probably would make any modern engine run like crap. Lead was introduced into gas in the 1920s, IIRC.
However, if you’re willing to do some minor adjustments to your gas engine, you can run it (not very well, but probably better than 1896-era gas) on pure-grain alcohol. Which would mean that so long as you could find an alcohol distiller, you’d have fuel (probably some time in the 1700s, I’m WAGging).
Alcohol should do it, but there will be a high percentage of water (10%+?) due to the distilling process and alcohol’s habit of ‘liking water’ (forgot the technical term) which may effect performance, especially if travelling at high speed is needed, say 88 mph.
Other then that natural gas (or LP gas) is usable in a gas engine also, and from what I’ve heard actually works better then gasoline. Capturing it and compressing it might cause a problem.
If it still has that Mr. Fusion installed, I would recommend making a trip fwd first to pick up the matter conversion adapter, this way you can make your own gas from dirt, twigs and fluffy animals.
I’ve read that the first adventurers to drive cross-country had no trouble finding fuel in even the remotest towns. Gasoline, or something close enough to it to be usable, was commonly sold by the can as cooking fuel by almost any general store. Even into the 40’s or perhaps later, many cars had low enough compression that they could run on (cheaper) kerosene after being started on gasoline.
Alcohol is hydroscopic (“water-seeking”) 
The word is hygroscopic. A hydroscope is somehting one uses to look into water, and hydroscopic pertains to hyrdroscopes.
Hydrophillic does indeed mean water loving, but it’s quite different to hygroscopic, which means water absorbing. We can talk for example about long china acetic acids, commonly called fats, which are mildly hygroscopic but by no stretch hydrophillic. Conversly many clays are hydrophilic while at the same time exhibing little or no hygroscopic ability.
Very different, though often related, characteristics.
Distilled alcohol was made by Islamic alchemists by the 9th Century AD, and in Europe by the 12th century AD. The proof was generally probably pretty low. However, anyone with a basic understanding of the distillation process would probably be able to manufacture 95% (190 proof) alcohol from whatever alcoholic beverages were available at the time. (Higher percentages cannot be obtained from distillation, but require other means).