Rectal: Poor and erratic absorption. Probably the worst route of administration.
Inhalation: These go directly to the site of action if not swallowed first. Probably one of the best routes of administration. If you’re treating an asthmatic, you’re getting it directly to the site of action, minimizing side effects. The only problem with inhalation is some people swallow the dose instead of inhale it into their lungs. Sometimes there are nasal inhalers that go through the nose instead of the mouth, such as for allergic rhinitis, corticosteroids and a few other drugs.
Sublingual/Buccal: Under the tongue or in the cheeks of the mouth.   Drugs can be absorbed very quickly and it avoids stomach acid. Nitroglycerine is given this way if the person is having chest pains. This will work within a minute or two.
Topical: Ointments, creams, patches, etc. Absorption is minimal and you’re putting it right on the site of action.  For this reason, creams and ointments are great for treating eczema, rashes, psoriasis, etc.
Subdermal: The patches are an ideal route of administration because the drug is being absorbed continiously. There are problems with having perfect blood levels at all times sometimes though. We administer subdermal patches that contain hormones, either postmenopausal or contraceptives.  And of course nicotine OTC. There are also narcotics available in patch form.
These patch drugs were intended for people such as cancer patients who can’t swallow, are in severe pain or have a very difficult time taking in anything. Today however the vast majority of people who use subdermal patches don’t have that problem.
What else can you think of in patch form?  The Exelon patch for treating Parkinsons. We even have medications for high blood pressure and that’s really unique cause it requires to be changed only once a week.