C64 doesn't have mode numbers (there's no BASIC or OS support for graphics). There are basically 5 real modes though :
Character mode - 40x25 character display. 256 8x8 2 colour characters, one colour is unique, one is background colour.
Multi-colour character mode - 40x25 character display. 256 4x8 4 colour characters, one colour is unique, three are background colours.
ECM character mode - 40x25 character display. 64 8x8 2 colour characters, one colour is unique, choice of 4 background colours.
Bitmap - 320x200 bitmap. 2 unique colours per 8x8 block.
Multi-colour bitmap - 160x200 bitmap. 3 unique colours per 4x8 block, 1 background colour.
I'm assuming you're mainly interested in bitmap mode. In that you have 8k of bitmap, bytes are in the same order as the Beeb but bits in multi-colour aren't - rather than 12341234 it's more like 11223344. Then you have a 1k 'video matrix', this doesn't have to follow the bitmap but usually does. Each byte is a pair of nybbles, giving 2 of the unique colours - 0 and 1 in standard bitmap mode, 1 and 2 in multi-colour bitmap mode. Then multi-colour mode has an extra 1024 nybbles containing colour 3, but these have to go at a fixed address of $D800. Then colour 0 comes from a VIC register.
All modes have the same 16-colour palette, it's at
http://en.wikipedia.org/wiki/File:VIC-II_color_map.svg.
There are a few software 'extended' modes, eg
FLI - 136x200 bitmap. 3 unique colours per 4x1 block, 1 background colour.
SuperHires - 96x167 bitmap. 2 'global' colours, 2 unique colours per 8x8 block.
There are loads more software modes, but they tend to be more limited in what colours you can have where. Most are described at
http://www.studiostyle.sk/dmagic/gallery/gfxmodes.htm if you're interested...
