Hobbies And Interests
Childhood
In real life people are molded by their childhoods, and so your character's childhood is an important starting place for understanding the person he is now. For example, did his parents die when he was young? He may have become self-sufficient and street-smart as a result, or he may have developed abandonment issues and will cling on to other characters. Did he grow up poor? His main goal in the campaign may be to accumulate riches so he won't go hungry again, which could clash with other characters' goals.
Alignment
The alignment system in D&D is a metaphysical reality, not just a roleplaying guideline. Certain spells affect some alignments and not others. You'll find it easier to roleplay your character's alignment, however, if you understand how it got that way. For example, did your character lose people she loved to violence? She might become neutral-evil, caring only about her desire for revenge, or she might become lawful-good, seeking to destroy evildoers by upholding the law. Does your character have a self-serving moral code? She might become chaotic-neutral, focusing on her own goals without any particular desire to do good or evil; or she might become chaotic-evil, not caring who gets hurt on her way to fulfilling her personal goals.
Relationships
How your character interacts with other characters is an important part of gameplay. For example, is your character friendly? He might immediately feel comfortable in a new party, and make the people around him feel comfortable as well. Does your character have a dark secret? He may be aloof around other people and evasive about his past, making him seem suspicious to others. Does your character have a significant other waiting for him? That will affect how he interacts romantically with both player characters and NPCs.
Career
It's tempting to just say your character is an "adventurer," but try to go deeper than that. Talk to the Dungeon Master about the story setting and figure out a realistic explanation for why your character is there. For example, if your character has a background as a hunter, she might have gotten run out of her last home for accidentally killing a sacred animal. If she's a scholar, she might be in a large city to conduct research at their libraries. If she's an alchemist, she might be peddling her wares, or have just lost her wares to a gang of thieves. Consider taking ranks in the "Profession" skill so your character's skill rolls can reflect her professional background.