Asking which brand has the widest soccer cleats gets you a bad answer, because the differences inside a brand are bigger than the differences between brands. adidas, Nike, Puma and Mizuno all make a roomy line and a narrow speed line, and the two do not fit alike even when they share a logo.
Take Nike. The Phantom has a high toe box and a wide forefoot, while the Mercurial is built low and narrow on purpose. At adidas the Copa leans roomy and the F50 leans tight. Puma follows the same pattern with the King against the Ultra. Mizuno has the Morelia II on a wider last and knit speed models that fit snug. New Balance is the exception: it sells declared wide widths (2E) on selected models.
Each brand page below goes line by line, with the size tip, the material and the surface options, so you can see which lines are worth a try. If you want a quick view of every model at once, the width map sorts them from narrow to wide. If you already know your foot, the cleat finder narrows it down further, and the wide soccer cleats guide explains what to check on any pair.