Pensieve Memories

Memories can be physically removed from a wizard’s mind with a wand and placed in a container or the Pensieve.

Pensieve Memories:

• Dumbledore’s memory of the Death Eater Trials, including those of Igor Karkaroff, Bellatrix, the Lestrange Brothers, and Barty Crouch Jr. (GF30)
• Dumbledore’s memory of 16-year-old Bertha Jorkins following a boy who met with a girl named Florence and being hexed by him  (GF30)
• Dumbledore’s memory of Snape talking about his Dark Mark returning (GF30)
• Snape’s “worst memory” of being attacked by James and Sirius, and calling Lily a “Mudblood” when she came to his defense (OP28)
• Dumbledore’s memory of Sybill Trelawney making a prophecy about Harry and the Dark Lord (OP37)
• Bob Ogden’s memory of trying to arrest Morfin Gaunt for hexing a Muggle, and meeting his father Marvolo and sister Merope Gaunt (HBP10)
• Caractacus Burke’s memory of Merope selling Slytherin’s Locket (OP13)
• Dumbledore’s memory of meeting with Tom Riddle for the first time at the Orphanage (OP13)
• Morfin Gaunt’s memory of meeting Tom Riddle, when Tom stole the Peverell Ring and then killed his father and grandparents in the Riddle House (HBP17)
• Slughorn’s memory of Tom Riddle asking how to make a Horcrux, both the tampered version and the clear version (HBP17, HBP23)
• Hokey the house-elf’s memory of Tom Riddle visiting her mistress Hepzibah Smith in order to steal the Hufflepuff Cup (HBP20)
• Dumbledore’s memory of Tom Riddle as a young Lord Voldemort requesting to be hired as Defense Against the Dark Arts teacher (HBP20)
• Severus Snape’s life memories left to Harry after his death, including his childhood with Lily and Petunia (DH33)

• A memory is "neither gas nor liquid" but something else resembling "light made liquid - or like wind made solid" (GF30, OP24, DH32)
• Memories are removed from the mind using a wand pointed at the wizard's head as they are slowly pulled out, and resemble silvery-white threads, or "gossamer strands":

Harry saw that it was in fact a glistening strand of the same strange silvery-white substance that filled the Pensieve. Dumbledore added this fresh thought to the basin, and Harry, astonished, saw his own face swimming around the surface of the bowl. Dumbledore placed his long hands on either side of the Pensieve and swirled it, rather as a gold prospector would pan for fragments of gold (GF30).

Snape merely raised the wand to his temple and placed its tip into the greasy roots of his hair. When he withdrew it, some silvery substance came away, stretching from temple to wand like a thick gossamer strand, which broke as he pulled the wand away from it and fell gracefully into the Pensieve, where it swirled silvery-white, neither gas nor liquid (OP24).

• Memories can be shared and stored in bottles for later perusal (HBP13, DH32). Dumbledore used "crystal phials" while Hermione conjured a bottle "out of thin air" to hold Snape's memory. A stopper holds in the memory - if not perhaps it might somehow escape.
• When Harry first looked into one of Dumbledore's memories in the Pensieve, he compared it to watching the memory of Myrtle's death in Tom Riddle's Diary. And it's true that Tom Riddle said he placed a memory in the Diary (CS13), but the diary was also a Horcrux containing part of his soul and therefore cursed. A torn bit of soul in a Horcrux and a thread of memory are two separate things.
• Horace Slughorn was ashamed that he had given Tom Riddle information about how to make a Horcrux, so he tampered with the memory to cast himself in a better light. That memory appeared to have "congealed" as if it had "gone bad" in the bottle, and there was a strange fog over the scene (HBP17). With the help of the potion Felix Felicis, Harry was able to prey on Slughorn's guilt and persuade him to hand over the real memory (HBP22, HBP23).
• Harry's final use of the Pensieve was to watch the memories Snape had given him as he was dying in the Shrieking Shack (DH33, DH34). Those memories of Snape's childhood and lifelong love for Harry's mother Lily were the catalyst for helping him to sacrifice himself in the Forest in order to save his friends, and to face Voldemort one last time to reveal that Snape's love was a true flaw in his plan (DH34, DH35).

Memories in the Pensieve are accurate and objective, according to the author:

It's reality. It's important that I have got that across, because Slughorn gave Dumbledore this pathetic cut-and-paste memory. He didn't want to give the real thing, and he very obviously patched it up and cobbled it together. So, what you remember is accurate in the Pensieve.

. . . that's the magic of the Pensieve, that's what brings it alive.   ...Otherwise it really would just be like a diary, wouldn’t it? Confined to what you remember. But the Pensieve recreates a moment for you, so you could go into your own memory and relive things that you didn't notice the time. It’s somewhere in your head, which I'm sure it is, in all of our brains. I'm sure if you could access it, things that you don't know you remember are all in there somewhere. (TLC)