Sweet Corn
Corn stubble is the main overwintering site for the fungus that causes head blight (scab) in wheat, which bleaches spikelets and taints grain. Keep wheat out of beds that grew corn, and do not plant the two side by side.
Barley
Barley and wheat host the same rusts, powdery mildew, and the aphid-carried yellow dwarf virus, so planting them together stacks the risk and lets infection jump between stands. Separate them by bed and by season.
Oats
Oats share wheat's grain aphids, the yellow dwarf virus they carry, and head blight. Growing them adjacent keeps a green bridge of hosts alive all season and raises disease pressure on both crops.
Teff
Wheat shares the rust and smut diseases of grain grasses, and volunteer wheat can carry spores over to a nearby teff patch. Plant them apart and clear grass stubble and volunteers before sowing teff.
Oregon Grape
Shrubs in the barberry family are the alternate host for stem rust of cereals: the fungus completes one stage on the shrub's leaves and moves to nearby wheat. Keep Oregon grape well away from grain, and check local rules — some regions restrict planting.
Rye
Wheat and rye host the same leaf rust, powdery mildew, and Hessian fly, so side-by-side plantings let problems build and carry over. Keep them in separate beds and separate rotation slots.