Weeds
When fall hits, so does ragweed, mugwort, and English plantain. To keep them out, leave windows shut as much as possible. Try rinsing off (or showering) and washing out your nose with a saline nasal wash when you come home. An air filter can help, too.
Cats
Feline allergen is particularly “sticky,” meaning that saliva and dander grabs onto everything—like subway seats—and then attaches to you. An air filter can help at home, but if you live with a kitty, immunotherapy shots might be your best choice.
Dust
It’s not so much dust as the dust mite. Vacuum carpets regularly. Use dust-mite-proof pillow and mattress covers to create a barrier between you and dust. Wash A/C filters often or put filters on the central air vents.
Molds
Particularly bad in early fall. If you suspect a fungi invasion, have the landlord call a mold remover. Then throw out old shower curtains and bath mats and go over moist areas with a disinfecting cleanser.
Dogs
It’s usually sufficient to avoid contact with them. Short-term (you’re staying with a dog-owner for a weekend), some Claritin is fine. Long-term (your girlfriend just bought a puppy), look into prescription meds or shots.
Cockroaches
Their bodies, feces, and saliva are all fairly common allergens. Ridding your home of the pests is the main thing, so do the usual: Clean out cabinets, call an exterminator, and plug up holes around baseboards and pipes.