This is another one of those “classic” combinations with a strong flavor overlap and a decent amount of mechanical overlap as well. Both of these classes are deeply tied to subversion, mischief, and rule-breaking in their default interpretations. Aside from the usual caster/non-caster problems, they mix fairly well on a mechanical level as well; both classes want Dexterity and the rogue certainly can find a use for Charisma. The real decision is how much sneak attack or how much spellcasting you want to give up in pursuit of the other.
Despite the default flavor leaning hard towards a Jack Sparrow-style charismatic scoundrel, backgrounds and archetype choices can take this in some interesting directions. When you come down to it, this combination is about social and covert skills, supporting others, and magic. That’s a fairly open palette to paint with.
Focusing more on rogue levels will give you a fairly standard stealthy character with a lot of precision damage and covert skills who can also turn on the charm and perhaps augment their existing stealth and subterfuge with a bit of the magical variety. A stronger focus on bard levels represents a charismatic character that knows when to get out of the spotlight and what to do once in the shadows. A more even mix gives you a wide variety of tricks, covert skills, spells, and support talents to draw upon. You will probably almost never be the best at anything, but you will be second-best at quite a lot.
[[Synergy Feats for Multiclassers#Bard w/ Rogue|Bard-Rogue chains and ideas]]