From a logical pov, I always add the comma in this situation - it's referred to as a "Serial Comma."
So, your sentence would look like apple, banana, and orange.
It depends really on when two objects are necessarily bound by the "and" or not. Contextually, the serial comma usually can be dropped without loss of meaning. Indeed, the trend has been to not place a comma.
However, I was trained in symbolic logic and, trivial as it may be, I always add it by habit - it doesn't take away from the meaning by putting it there, but there might be a situation where confusion does arise by its absence (albeit rare). Ultimately, it comes down to whether you are bound by a specific style manual, and if not, whether you prefer to use it or not.
Like I said, I had it drilled into my mind to use it; similarly, I had the double space after a period drilled into my mind - and popular opinion on using that seems to mean I'm from the 1920s...(?). Regardless, I can't help myself using the double space following a period. So, if you don't want to have to argue it to fisticuffs in a decade, it might be best to yield to popular usage (or popular non usage) of the comma in this situation.
The biggest issue, in my mind, is consistency. If you choose to use the serial comma once, then you should use it all the way through whatever you are writing.
Edit - this is not the same question as a pertaining to placing a comma in a list - that holds a stronger claim to the serial comma's usage. This is not listing off items. For instance, when referring to people, there are often relationships between two individuals that exist separate from the other(s). So in Bill & Ted's Excellent Adventure, George Carlin plays the character X. So a sentence might warrant the dismissal of the serial comma because Bill & Ted are a team. You would get something akin to "....X, Bill & Ted." You can add a comma - that's fine; but, as a duo, this would be a situation where the comma would be better withheld.