This was discussed in this topic
but I'll re-list the character cards that talk. (But I'm not going to reveal who talks to who though...)
From beginner's cards...
Lion Baron / Zagar
Killing Machine / LeBeau (Yes, he talks! Everyone was too busy using him for his SS, but you should try him and see what he'll say.)
Bellydancer / Kurina
Azure Dragon / Vordore
And from basic sets...
Solar Prince / Verlaat, Saber Saint / Lapierre, Zombie Lord / Zugaterosa, Abyss Centaur / Dical, Chaos Lady / Annarose, The Red Mantle / DeFau, Lightning Samurai / Thunderbolt, and Wise Swordsman / Steel.
Have fun finding out what they say!