Except in the case of 3D print bed that tilt, most FDM printers print the layers horizontally, which affects a few parameters of the printed part, including the strength, quality, print speed and cost of the print.
It’s easier to pull a bun off of a hamburger than it is to tear the burger in half for sharing. The same strength orientation considerations apply to the horizontal 3D printed layers in FDM. In the case of tension being oriented perpendicular to the layers, the part is weaker:
In the case of the tension being in the direction parallel to the layers, the part is stronger:
In thin load-bearing features, orientation significantly affects strength, because they translate to tension being applied either parallel or perpendicular to the layers.
For example, in the picture below, if the layers in the column are oriented like the column on the right, it will be strong and flexible under that shear force (green arrow), and weak if layers are oriented like the column on the right:
That's because the layers are horizontal, which is parallel to the force. The result is a shear force that sort of peels the layer apart:
Which is why the part on the left failed, but the one on the right didn't fail:
These were the same part, printed in two different orientations.
Orientation should produce the least number of overhangs. Notice how certain parts are easily reoriented to reduce overhangs:
3. Support Requirements (More material=more cost=slower print)
The orientation heavily affects support requirements. More supports takes more material, which costs more, and takes more time to print. So it's worth playing around with the orientation to see how it affects print speed, material usage, and cost:
The use of support not only requires you to remove supports from the part, but it also leaves residual surface defects which affect overall quality (and require post-processing). These surface quality issues can make it difficult to assemble parts.
For example, parts with a round cross section that are printed directly against the print bed (without supports) result in a cross-sectional bulge near the print bed. So a round peg, for example, may no longer fit properly in a round hole. So spherical and cylindrical objects printed parallel to the bed should be printed vertically or with supports (which still compromises surface quality).