If paper doesn’t feed through your Epson printer, look out for the following:
Leading edge problems. If there’s anything wrong with the leading edge of the paper (the edge that goes in first), the printer may not be able to load it. Check for creases, folds, tears, or other damage. Proper loading depends on the leading edge being perfectly even, so that it goes straight into the rollers. If the leading edge is damaged, try turning the paper around and loading the edge on the opposite side instead. If for some reason that’s not practical, do your best to smooth out the edge. This problem is more likely to happen with paper that was reused or damaged.
Paper curl. If the paper curls the wrong way (outward compared to the rollers), the printer rollers might not be able to grab it. Remove the paper and see if it has a curl at the edge. If it’s printable on both sides you can try printing on the other side so that the curl goes the other way. If it’s coated on only one side, you’ll have to carefully try to de-curl it. If it’s expensive fine-art paper, use great care to avoid creasing it or leaving fingerprints when you try to remove the curl. The expensive solution is to use a deroller; this is typically used by people who buy paper in rolls since those tend to make the curl quite persistent.
Friction with other sheets. If you’re loading multiple sheets at a time, the frontmost sheet might not drop into the rollers if it sticks a little to the next sheet in the stack. Try jostling and fanning the paper stack to loosen them up. This is more of a problem with papers with some types of coatings and textures.
Dirty rollers. House dust or dust from matte or rough fine art papers can build up on the rubber rollers, reducing their grip and making it harder for them to grab the paper. If a cleaning sheet is available for your printer you can try that. If you don’t have a cleaning sheet, try picking up the dust off the rollers by pressing a piece of moderately sticky paper on them. (Don’t use something that’s so sticky it might ruin the rollers, like packing tape, address labels, or duct tape.)
If the printer continues to have trouble grabbing the paper, as the print job starts try holding the paper and give it a slight nudge in as it loads.
Narrow paper. On the Epson Stylus Pro 3800, the manual feed slot doesn’t like paper that’s much narrower than a US Letter sheet. You’ll have to feed it through the automatic feeder. But the automatic feeder may have trouble with paper smaller than 4 x 6 inches; you may have to keep it straight with your hands as it drops into the slot.
Black area of paper. On the Epson Stylus Pro 3800, there’s an odd issue where the Epson 3800 may not sense the paper correctly if part of the paper is already covered with black. Read about that in this article: Epson 3800 error: Incorrect paper size or Paper error.
I’ve only used Epson printers, but those tips may also apply to other brands of inkjet printers.