Ribbons share no significance in Generation V.
But in the upcoming Generation III remakes, Ribbons might once again become important. The original Ruby and Sapphire games had Pokemon Contest, and even a museum where a painter painted the your pokemon if it won the highest level of competition in a specific area.
But other than that, They're just bragging rights.
(My Blaziken was painted).
It won in Beaty and Coolness in both Emerald and Diamond!