Well...
My cat Willy always greeted me at the door. When his hearing started to fail he began waiting for me in the window. He did that right up until he was put to sleep at the age of 21. The former feral Heidi (Willy's cat) would also come out to greet me, go back into hiding, and come back out. Linus and Lucien (my current cats) have the following routine:
I walk in and make my way down the hall to the living room
Linus comes out from the bedroom or office, circles the room, scratches on the scratching block, and then rubs up against my leg. If I'm sitting on the sofa he jumps up and rubs against my hand or my face
Lucien follows Linus and does the same circle, scratches the scratching post, rubs against my leg, and jumps on my lap.
The two cats purr up a storm while they take turns licking me
On the off chance that I come in and they don't hear me, they run around meowing and then do the normal routine. It is as if they are embarrassed for not coming to me.
Cats are very affectionate creatures when they are show affection. This does vary by breed. Scottish Folds, like Willy, are known to latch onto a person. Russian Blues and Korats (L&L have Russian Blue and possibly some Korat in them) are also affectionate and latch onto one person. They are also talkers, which Linus and Lucien both are.