Two Situations
Here are some situations whereby you might find casual games on handheld consoles to be quite handy. I can only think of two at the moment.
1. Babysitting kids
The game is not for you to play with, but rather it's for the kids. If you are babysitting a hyperactive child or basically any kid that has already been exposed to video games, chances are you will have a better chance of keeping the kid occupied with a video game rather than with anything else. If your underage charge starts asking for Grand Theft Auto instead of Mario Kart DS, tell him that playing the game will make him go to hell. Kids are gullible that way.
2. Waiting for your date
Waiting is probably the activity that you do most when you are dating someone who is either a vain pot or a metrosexual. They tend to spend A LOT of time in the bathroom or in front of the dressing table before stepping out with you.
It is normal to be feeling excited over how your date will look like but this only happens at the start of the relationship, the feeling of excitement will soon be replaced with boredom. Short games on your PSP or Nintendo DS will help alleviate your suffering.