I've noticed that some people have trouble getting colors of the characters right (especially those with various vision problems), so I thought I'll help by giving you some color values. They were taken from official arts, but they are approximate so don't flame me XD
SEGA artists themselves don't use exactly same colors all the time for some reason (just very similar shades). Guess they didn't bother to save all the values.
I won't state obvious colors, like plain old white and black.

Sonic:
Fur (Modern) – RGB 26, 80, 188; HEX #1A50BC
Fur (Classic) – RGB 13, 122, 233; HEX #0D7ADF
Skin (Modern) – RGB 255, 215, 143; HEX #FFD78F
Skin (Classic) – RGB 255, 224, 177; HEX #FFE0B1
Eyes – RGB 0, 213, 0; HEX #00D500 and similar shades
Shoes –RGB 255, 0, 0; HEX #FF0000
Shoe Buckles – RGB 255, 207, 0; HEX #FFCF00

Tails:
Fur - RGB 241, 176, 0; HEX #F1B000
Eyes - RGB 15, 179, 240; HEX #0FB3F0 and similar shades
Shoes - RGB 255, 0, 0; HEX #FF0000

Knuckles:
Fur and red shoe part – RGB 255, 20, 0; HEX #FF1400
Eyes – RGB 95, 63, 170; HEX #5F3FAAand similar shades
Green shoe part – RGB 1, 170, 51; HEX #01AA33
Yellow shoe part – RGB 255, 210, 0; HEX #FFD200
Gray shoe part and soles – RGB 170, 170, 170; HEX #AAAAAA
Skin – RGB 255, 221, 160; HEX #FFDDA0

Amy:
Fur – RGB 253, 149, 198; HEX #FD95C6
Eyes – RGB 1, 169, 0; HEX #01A900
Dress, shoes, hammer and other red parts – RGB 209, 0, 0; HEX #D10000
Bracelets and yellow part of the hammer - RGB 255, 210, 0; HEX #FFD200
Hammer's handle 1st part – RGB 235, 151, 0; HEX #EB9700
Hammer's handle 2nd part – RGB 175, 92, 0; HEX #AF5C00
Skin – RGB 254, 220, 149; HEX #FEDC95

Shadow:
Any red part, including eyes: RGB 220, 0, 0; HEX #DC0000
Inhibitor rings and thruster thingies on the shoes – RGB 255, 210, 0; HEX #FFD200
Skin – RGB 255, 181, 40; HEX #FFB528

Rouge:
Eyes – RGB 14, 160, 150; HEX #0EA096 and similar shades
Pink cuffs and hearts – RGB 250, 130, 186; HEX #FA82BA
Wings – RGB 50, 29, 60; HEX #321D3C
Blue eye shadow – RGB 0, 160, 230; HEX #00A0E6
Skin – RGB 255, 170, 41; HEX #FFAA29
Darker skin in the ears – RGB 240, 140, 20; HEX #F08C14

Cream:
Light cream fur – RGB 255, 230, 190; HEX #FFE6BE
Orange fur – RGB 255, 139, 0; HEX #FF8B00
Eyes and nose – RGB 141, 89, 41; HEX #8D5929
Dress and shoes – RGB 255, 90, 0; HEX #FF5A00
Yellow part of the shoes and buttons on the cuffs – RGB 254, 225, 0; HEX #FEE100
Blue bow – RGB 127, 211, 248; HEX #7FD3F8

Dr. Eggman:
Suit – RGB 241, 10, 0; HEX #F10A00
Moustache – RGB 210, 111, 10; HEX #D26F0A
Glasses – RGB 30, 33, 136; HEX #1E2188
Cuffs – RGB 247, 171, 0; HEX #F7AB00
Buckle thingies on the suit – RGB 255, 210, 0; HEX #FFD200
Green lenses in goggles – RGB 62, 183, 55; HEX #3EB737
Nose – RGB 249, 80, 99; HEX #F95063
Skin – RGB 255, 196, 146; HEX #FFC492

Blaze:
Fur – RGB 218, 195, 237; HEX #DAC3ED
Dress and purple fur – RGB 143, 100, 205; HEX #8F64CD
Shoes and trim on the dress – RGB 240, 20, 130; HEX #F01482
Forehead gem and ring – RGB 231, 0, 14; HEX #E7000E
Eyes and necklace – RGB 255, 180, 0; HEX #FFB400
Inner ear skin – RGB 255, 230, 120; HEX #FFE678

Silver:
Fur – RGB 231, 237, 233; HEX #E7EDE9
Eyes and bracelet thingies – RGB 255, 180, 0; HEX #FFB400
Cyan part of the shoes – RGB 0, 152, 150; HEX #009896
Dark blue part of the shoes – RGB 0, 20, 79; HEX #00144F
Red gems on the shoes – RGB 210, 12, 34; HEX #D20C22
Skin – RGB 248, 182, 59; HEX #F8B63B

Vector:
Light green skin – RGB 220, 255, 103; HEX #DCFF67
Darker skin – RGB 57, 164, 0; HEX #39A400
Stripes on the shoes and cuff thingies, also eyes – RGB 249, 175, 0; HEX #F9AF00
Buckles and chain – RGB 255, 210, 0; HEX #FFD200
Scale thingies on the back – RGB 220, 82, 17; HEX #DC5211

Espio:
Magenta skin/scales – RGB 201, 0, 140; HEX #C9008C
Shoes and shields on the gloves – RGB 100, 20, 131; HEX #641483
Horn, eyes and buttons - RGB 255, 180, 0; HEX #FFB400
Skin – RGB 255, 210, 129; HEX #FFD281

Charmy:
Orange on the jacket, shoes and goggles – RGB 255, 134, 1; HEX #FF8601
Yellow stripes - RGB 100, 20, 131; HEX #641483
Trim on the helmet – RGB 218, 0, 1; HEX #DA0001
Eyes – RGB 249, 175, 0; HEX #F9AF00
Wings – RGB 211, 237, 250; HEX #D3EDFA
Skin – RGB 254, 214, 142; HEX #FED68E

Omega:
Red parts – RGB 230, 10, 10; HEX #E60A0A
Yellow parts – RGB 100, 20, 131; HEX #641483
Green parts – RGB 100, 178, 32; HEX #64B220