Just two, that we grow, come in mind right now - mint, that's great for tea/curing cold and black radishes. Black radishes are interesting, they have an awesome spicy taste but if you cut a hole in one and put some sugar in the juice that results is great for throat ailments. Worth mentioning is garlic that's great to consume in winter as it builds your resistance to colds (or so I've been told).
Fresh basil leaves can be steeped in a cup of boiling water to make a tea, which will clear up congestion when you have a cold. I've done this a few times when I was too run down to go to the drug store to get some medicine, and I happened to have a bunch of fresh basil in my fridge. It really does work, and quickly too. But the results are only temporary, so it's not like taking medicine that stays in your system for several hours. My dad recently came down with a cold, and we tried going the oregano route, but the health food stores I went to wanted an arm and a leg for Oregano Oil in a bottle or in pill form, it's like $50 a bottle! I am under the impression you would need a lot of fresh oregano to see any benefits from it.
Not sure if this counts, but when I get sore eyes, I put steeped tea bags on them. Just let them cool for a while. It has antiseptic properties and it is very soothing. My friend who taught me this chills them first, but I find that warm works better for me.
I am amazed on a regular basis at the healing capacity of plants that I never thought of as having any such qualities. If people spent more time learning about and growing their own edible and medicinal plants, there would be a lot less illness in the world.
