...the sort of old woman that's married to a guy named "Richard", and everyone hates being around her? It always goes to these neighbors, which one is a fat guy who wears a cap, and his wife is fat too. And some other woman often comes in to their living room. And, I don't think there's a Live Audience in this show. Is this "Keeping Up Appearances"?

'Keeping Up Appearances' does have Hyacinth's husband Richard and sister Daisy? and brother-in-law, Onslow who I think may have had a cap at some point (tho I think it's Richard who is usually wearing one). Elizabeth and Emmet Hawksworth? are the neighbors. Hope this is of some vague help!!!!!!!!!!!

Yeah, that's the one I'm thinking of. I like "Are You Being Served?" better, but this one's pretty funny.

Another question:

What's the weirdo one where these people are in a spaceship and there's this giant face that talks to 'em?

Red Dwarf. The 'giant face' is their shipboard computer, Holly. But it's not weird! :)

Ohhh, so THAAAT's "Red Dwarf". It's pretty popular.