Originally Posted by OotP

PAGE 49: "And this is Nymphadora -"
"Don't call me Nymphadora, Remus"
"Nymphadora Tonks, who prefers to be known by her surname only," finished Lupin.
"So would you if your fool of a mother had called you Nymphadora," muttered Tonks.
PAGE 57: Lupin and Tonks followed, carrying Harry's trunk between them.
(Lots of Remus/Tonks interaction like this. JKR likes to put those two together)
PAGE 112: Lupin and Tonks sitting there.
PAGE 113: Lupin glanced at Harry, then said to Tonks, "What were you saying about Scrimgeour?"
(Noticing Harry's discomfort, but wanting to continue his conversation with Tonks)
PAGE 764: Next to Tonks was Lupin.
PAGE 765: "Anyway, that's not the point," interjected Tonks. "The point is, if we find out you've been horrible to Harry -"
"- And make no mistake, we'll hear about it," added Lupin pleasantly.
(Once more, the fun banter of finishing each other's sentences)

Originally Posted by HBP

PAGE 82: "I'd better be off," she [Tonks] said quickly, standing up and pulling her cloak around her shoulders. "Thanks for the tea and sympathy, Molly."
(We now know from the rest of the evidence that Tonks was probably talking to Molly about her woes regarding Lupin and their relationship).
"Dear, why not come to dinner at the weekend, Remus and Mad-Eye are coming-?"
(Molly trying to woo Tonks to dinner to spend time with Remus.)
PAGE 95: "I know Lupin tried to talk her [Tonks] round, but she's still really down. She's actually having trouble with her Metamorphosing!"
(We don't know exactly why Tonks is feeling down, but if it has anything to do with Lupin, chances are his talking to her didn't help much. Also, if you notice she's having problems morphing/magic. Dumbledore made mention that unrequited love can alter magic as well.)
PAGE 132: "She 'as let 'erself go, zat Tonks," mused Fleur, examining her own stunning reflection in the back of a teaspoon. "A big mistake, if you ask -"
"Yes, thank you," said Mrs Weasly tartly.
PAGE 157: "No problem," said Tonks, without smilling. From what Harry could see in the darkness, she was as mousy-haired and miserable looking as she had been when had met her at The Burrow.
PAGE 157 & 158: "As Harry swung the cloak back over himself she waved her wand; an immense silvery four-legged creature erupted from it and streaked off into the darkness.
"Was that a Patronus?" asked Harry, who had seen Dumbledore send messages like this.
"Yes."
(We learn that Tonks's Patronus is a silvery, four-legged creature which we could assume was Padfoot, but the hint of "silvery" is a clue that it's a wolf.)
PAGE 160: "And incidentally," said Snape, standing back to allow Harry to pass him, "I was interested to see your new Patronus." He shut the gates in her face with a loud clang and tapped the chains with his wand again, so that they slithered, clinking, back into place.
"I think you were better off with the old one," said Snape, the malice in his voice unmistakeable. "The new one looks weak."
As Snape swung the larntern about Harry saw, fleetingly, a look of shock and anger on Tonks's face. Then she was covered in darkness once more.
(This Patronus is new, though we don't know what her old one was. Another hint that the new Patronus looks weak. Remus is often described as appearing weak.)
PAGE 340: "You are as bad as zat Tonks," said Fleur to Ron, when she had finished kissing Bill in thanks, "She is always knocking -"
"I invited dear Tonks to come along today," said Mrs. Weasley, setting down the carrots with unnecessary force and glaring at Fleur. "But she wouldn't come. Have you spoken to her lately, Remus?"
"No, I haven't been in contact with anybody very much," said Lupin. "But Tonks has got her own family to go to, hasn't she?"
"Hmm," said Mrs Weasley. "Maybe. I got the impression she was planning to spend Christmas alone, actually."
She gave Lupin an annoyed look, as though it was all his fault that she was getting Fleur for a daughter-in-law instead of Tonks.
PAGE 340: "Tonks' Patronus has changed its form," he told him [Lupin]. "Snape said so, anyway. I didn't know that could happen. Why would your Patronus change?"
Lupin took his time chewing his turkey and swallowing before saying slowly, "Sometimes ... a great shock ... an emotional upheaval ..."
"It looked big, and it had four legs," said Harry.
(Harry isn't aware of Remus and Tonks's relationship, or unrequited love if that's the case, and isn't aware that her Patronus is a wolf. Remus seems to think about this information carefully before revealing too much. The emotional upheaval could be Sirius' death, or something that happened between he and Tonks)
PAGE 465 & 466: "Harry?" He spun round, one-legged, and toppled over. There, to his utter astonishment, was Tonks, walking towards him as though she frequently strolled up this corridor.
"What're you doing here?" he said, scrambling to his feet again; why did she always have to find him on the floor?
"I came to see Dumbledore," said Tonks. Harry thought she looked terrible; thinner than usual, her mouse-coloured hair lank.
"What did you want to see him about?"
"Nothing in particular," said Tonks, picking, apparently unconsciously, at the sleeve of her robe. "I just thought he might know what's going on...I've heard rumors...people getting hurt..." [...] "You haven't had any letters from anyone in the Order recently?"
"No-one from the Order writes to me any more," said Harry, "not since Sirius -" He saw that her eyes had filled with tears.
(Harry thinks she's upset about Sirius, which she very well may be, but we later find out that Tonks was checking with Dumbledore to make sure Lupin was safe after hearing about a Greyback attack. She hadn't heard any news from the Order and was worried for Remus.)
PAGE 623 & 624: "You see!" said a strained voice. Tonks was glaring at Lupin. "She still wants to marry him, even though he's been bitten. She doesn't care!"'
"It's different," said Lupin, barely moving his lips and looking suddenly tense. "Bill will not be a full werewolf. The cases are completely-"
"But I don't care either, I don't care!" said Tonks, seizing the front of Lupin's robes and shaking them. "I've told you a million times ..."
And the meaning of Tonks's Patronus and her mouse-coloured hair, and the reason she had come running to find Dumbledore when she heard a rumor that someone had been attacked by Greyback, all suddenly became clear to Harry; it had not been Sirius that Tonks had fallen in love with after all ...
"And I've told you a million times," said Lupin, refusing to meet her eyes, staring at the floor, "that I am too old for you, too poor ... too dangerous ...'
'I've said all along you're taking a ridiculous line on this, Remus," said Mrs Weasely over Fleur's shoulder as she patted her on the back.
"'I am not being ridiculous," said Lupin steadily. "Tonks deserves somebody young and whole."
"But she wants you," said Mr Weasley, with a small smile. "And after all, Remus, young and whole men do not necessarily remain so." He gestured sadly at his son, lying between them.
"This is ... not the moment to dicuss it," said Lupin, avoiding everybody's eyes, as he looked around distractedly. "Dumbledore is dead ..."
"Dumbledore would have been happier than anyone to know that there was a little more love in the world," said Professor McGonagall curtly, just as the hospital doors opened again and Hagrid walked in."
(Ah, the moment Remus and Tonks truly became canon. We find out all along it was Remus Tonks was really mourning and it seems they've had something going on for awhile. Could be it ended because of Sirius' death and Remus' fear of hurting Tonks? But we also see Molly and Arthur are both supportive of the relationship, as is McGonagall. It's quite clear that despite his misgivings, Remus cares for Tonks as much as she cares for him, and she doesn't care that he's a werewolf.)
PAGE 641: "Most Harry did not recognize, but there were a few that he did, including members of the Order of the Phoenix: [...] Tonks, her hair miraculously returned to vividest pink, Remus Lupin, with whom she seemed to be holding hands."
(Tonks and Remus are holding hands, and Tonks seems to have color in her life again, so it's safe to assume they've worked things out and are together.)