Most barcode complaints aren't actually about the barcode format at all — they're a sizing or print quality issue wearing a format complaint's clothes. A properly sized EAN13 on decent paper will almost always scan fine; a shrunk, blurry one won't, regardless of format.
The minimum size that actually works
As a rough floor, don't print a standard 1D barcode (EAN13, Code128) narrower than about 3cm wide — below that, the individual bars get thin enough that ordinary print resolution starts merging them together, especially on thermal printers.
Scaling matters more than absolute size
If you must shrink a barcode below its designed size, scale it down as a whole rather than only compressing its width — squeezing width while keeping height fixed distorts the bar ratios that scanners rely on to read the code correctly.
Leave the quiet zone alone
The blank margin on either side of a barcode isn't decorative — it's how a scanner knows where the code starts and stops. Don't crop it tight to save space; a barcode with its quiet zone trimmed off is one of the most common self-inflicted scanning failures.
Resolution matters as much as size
A correctly sized barcode printed at low resolution (a cheap inkjet on absorbent paper, for instance) can still blur enough to fail. If you're printing on standard office equipment, a laser printer generally holds sharper edges than an inkjet for this kind of fine-line graphic.
When in doubt, test it — don't guess
A minute spent scanning a single test print with your actual scanner, on your actual label stock, catches more problems than any general sizing rule. Print quality varies enough between printers and paper that "it worked for someone else" isn't a reliable guarantee.