He said - She said

My post today is about dialogue tags. You know the thing, she said, he said, she questioned, he replied.  The general criticism I've heard about these, is that their use pulls the reader out of the story. I've read that said is better than other words like replied, because the eye passes over it, although as a reader I don't really agree.
For me, good writing really flows well without tags at all. But it can be difficult to do.
Approach one: lines of dialog, without tags. Works for a while, but if used to excess, it can be difficult to keep track of who is speaking. Also, it doesn't reveal much of the pov characters feelings, or the other characters feelings. While you're living in the head of a character, you can't reveal what another character is feeling in any other way than their words and body language.
Approach two: Use action tags to show the characters action instead of a dialogue tag.
At this stage, I would be going 'huh?' so time for an example. This one is from one of my favourite Modern Heat writers, Robyn Grady. An excerpt from 'Naughty nights in the millionaire's mansion' (Thank you, Robyn!)

It's written in the heroine's POV. Vanessa. The red text is me.

Her gaze flicked to his left hand - large, tanned but no gold ring. Still, not all those who were taken wore bands. As she'd found out. (so from this we see she's interested, and has had a previous bad experience)
'Perhaps your wife could help.'
'I'm not married.'
'Girlfriend?' (see? lovely use of no dialogue tags. Just a ? at the end to indicate a question)
She was curious - only for the dog's sake. A workaholic man-god descended from warriors wouldn't be interested in an ordinary girl working her way up the ladder...lately one rung up, three rungs back. (lovely bit of information reveal, giving us Vanessa's internal thoughts, in her very distinctive pov voice)
'My housekeeper comes in once a week.'
She cut him a wry grin. (There you go, an action tag instead of a dialogue tag) Not the same.
She had a thought. (much better than sticking, she thought at the end) 'If a dog's too much responsibility and a fish maybe isn't enough, perhaps a -"
"Don't say cat." His chin and its deep cleft came down. "I don't do cats." (and we know how he feels because of the descriptive tag stating his body's response. No need for he said, or he warned, or any of those other dialog tags.)

Something to think about? Many thanks to Robyn for giving me the perfect example!