Title says it all, really. Do you consider x or y to be running forward/backward? Which one side-to-side?
In my mind, x has always sort of felt like the front/back axis, since it comes before y, and that’s sort of more “basic.”
Based on the blender default front and side view I see X as being side to side and Y as being front/back, but of course it really doesn’t matter what the axises are labeled as long as you understand which is which.
Also think of a standard 2d plot, X is side to side also, I always thought Y should be up and down though for the same reason.
Which view are you referring to? Top? Side? Front? Bottom? Left? Back?
you are in 3D so if you put the 4 viewports on your screen
you see the top view is the X-Y plane then the front view which is the Z-X plane
and the side view which is the Z-Y plane and the last one being the 3D at whatever angle you want to look at it
so don’t think in terms on 2D XY but more in the real world of blender which is 3D !
Salutations
Cool, sounds like people lean towards X being side-to-side and Y being lengthwise.
Partly I’m asking just out of curiosity, and partly because I’m writing a script that may treat one of the axes as the “front.” I figured I should get some data before making a decision. 
Sol Blue, pull down the User Preference window from the top of the screen, select the View and Controls button, then select “View Names.” This will give you the Blender standard names for the views Top, Bottom, Left, Right, Front, Back.
Should clear things up.
Welcome to BlenderArtists. 
Interesting question. I’m biased because Blender is just about the only place I actually have to worry about axes at all.
I believe that, as a rule, “X” is the globally accepted left-to-right axis. In math, when you’re using graphs, I was taught that the horizontal “axis” is always named first.
From what I understand, Blender’s convention is different from other 3D software. When I think about the world in which humans exist, I see a two-dimensional world. We can walk left and right, forward and backward. We can’t walk up and down. Indeed, we rarely look down, and almost never look up. So while we are three-dimensional, we see the world as flat.
Thus, to me, the “XY Plane,” as RickyBlender put it, would be laid out on the ground, with X going left to right, and Y going front to back. The rarely used Z axis gives the world depth, up and down. Stairs, elevators, airplanes, etc. help us shift between levels of elevation on the Z axis, but we’re only free to move along the “ground plane” – which in Blender, of course, is represented by a grid “floor.” Makes perfect sense to me. But then again, I only ever have to think about it in terms of Blender.
If you project your texture on the object, Blender’s way to calculate the projection is in direction of Z-axis. I feel you should keep with this, Z-axis pointing towards you or to the opposite direction.
Personally if I model a car or something like that, X-axis is always showing the width of the object. So cars are always mirrored along X-axis. Y-axis is in the direction of the length of car, and Z tells the height. I try to organize my screen always the same way, so that Num-7, Num-1, and Num-3 corresponds to the corners of my screen, so that I always know, how to easily restore the top-, front-, and sideviews, if they get lost when rotated.