Personal motivation, relationships, and background.
...and these three are very closely related & intertwined.
Draw on the background of your players. If you haven't made up any for them: it's never too late to sketch up and progressively detail and develop one. Make the NPCs matter to them through connections: family, organizations, society, similar situations, etc.
A little girl is dying of a disease, and her father, a nephew of one of the adventurers, asks the adventurers to get the cure... (If they don't help, their family might even disown them.)
A little girl is dying of a disease, and her father, the brother of the love interest of one of the adventurers, asks the adventurers to get the cure... (If they don't help, there goes the chance for romance. Heartache is a bad thing.)
A little girl is dying of a disease, and her father, the sheriff of the city the PCs are staying in, asks the adventurers to get the cure... (You don't want to cross the sheriff, if you intend to stay in his city. You might leave and never come back, of course...)
A little girl is dying of a disease, and her father, a poor, slightly mad scientist, capable of developing a cure for the entire village, asks the adventurers to get the resources for the cure. (If they deny him, the desperate people of the village might even attack them. Sure, you could slaughter the village... but that doesn't look good on your CV, usually.)
A little girl is dying of a disease, and her stepfather, a poor hermit, asks the adventurers who worship the same god, to get the cure... (If they don't help, their god might get slightly pissed off.)
Allow them refuse the call to adventure, then have them face the consequences. It should teach them a lesson. ;) After a few lessons, they'll consider their options more thoroughly. (Careful, don't overuse this. Let some refusals go without serious consequences. Such is life. Keep it real.)
So, the little girl died...
...two days later, her ghost starts haunting you. You can hardly harm it, and even if you kill it, it returns the next night. You start losing sleep (you get negative modifiers), and your weapons that touch her begin to corrode.
...and the disease has started to spread. Now a whole village is dying. And one of the PCs isn't feeling quite well either.
...and her father, the sheriff, who used to be a poor, slightly mad hermit dabbling in science, has put a curse on one of you. And he threw you in jail for a few weeks, so you missed that other, very important meeting.
...and her father got very sad, but you didn't give a damn. Heartless bastards. (As @Joe said.) So, here's a random encounter. ;]