The simplest and best verb for dialogue attribution is said. Plain and simple, and — as I think I’ve mentioned here before — effectively invisible. Other verbs like replied, stated, mentioned, affirmed, and the like are also valid, but should be used sparingly and in proper context. Replied only works when the speaker is responding directly to something somebody else has just said, for instance, and stated goes with declarative sentences in which a fact or opinion is being asserted.
And then there are the verbs which are not meant for dialogue attribution at all. Smile, for example. People don’t smile things, they say them. They may say them smilingly, or say them, smiling, but smile does not equal say and shouldn’t be used as if it does. The same goes for any other gesture or facial expression — no shrug or wink or grimace is the equivalent of speech.
I’m just sayin’.
Dr. Doyle's Blog 
Elementary-school teachers are far too fond of handing out a list of the entire thesaurus entry for “said” and encouraging their students to use ALL of them. And then writers have to break themselves of that habit later.
Worse, those lists go around tumblr, and inexperienced writers grab on to them as if they’re a good idea. Then other writers have to explain that they’re really, really not.
I’m just sayin’.
I wonder if part of the problem is fear that characters do not have distinctive voices. Less confident writers use more attribution of speech – rather than just for new speakers or key points – and want to avoid long strings of “he said.., she said…” so use purple prose to add variety.
Annalee smiled. “If you start with the gesture or expression, like this, then you don’t need a dialogue tag at the end at all, and you avoid ridiculous constructions in which people ‘smile’ and ‘shrug’ things.”
Perry nodded. “I see.”
“And if you put the tag in the middle of your dialogue,” Annalee said, “it indicates not just who spoke, but that they broke for a beat or pause.”
“It also keeps saids from laddering up at the end of every line of dialogue,” said Perry.
“And now that our respective roles in this conversation (and my verbal tic of starting sentences with ‘and’) have been established, readers should be able to figure out who’s saying this line without any tag at all.”
Susan slid into the booth next to Perry. “Since I’m a third person joining in, my arrival is noted.”
“Ah, Susan, good to see you! Perry said you might be joining us–and hey look, now the reader knows who’s speaking again, without the need for another tag.”
“Quite so,” Susan said, over the top of the breakfast menu. “Which only goes to show: if you want to avoid said-itis, you need to be intentional about structure, rather than over-thinking word-choice.”
The waiter cleared his throat and clicked his pen twice. “Our specials today include Asiago ‘As You Know, Bob’ Scrambled Eggs and Purple Prose Pancakes.”