On its website, Consumer Reports has posted a review and comparison of drain-cleaning products (PDF). The article is about ten years old, but it's free even for non-subscribers.
Out of all the products they tested, the Drain King VIP1 kit is one of their favorites. They say that it's worth keeping the kit on hand. It's very powerful. It uses water pressure (from an indoor or outdoor faucet) to clear drain clogs.
The product is not perfect, but is still useful. (The manufacturer warns: "Drain King should be inserted past any potential areas where water might vent out. If not possible, simply close or plug potential vents.")
Where I live, one of the toilets is clogged.
The manufacturer of the Drain King kit writes: "We do not recommend using a Drain King to unclog a toilet". Why not?