You're in a band. You've been looking for your guitar, and are surprised to discover that your bandmate is playing it. You're angry that he took the guitar without asking you first. You say:
You can't just go around using people's stuff without their permission!
You have a website where you post photographs that you've taken. You don't want people to take your photos and use them on other web sites without asking you, so you write at the bottom of the page:
Images on this site may not be used without my express written permission.
legal, modal, permission, photography, warnings, website, written English You want to take the day off work today because you went out drinking last night and you don't feel good this morning. You're writing an e-mail to your boss to let her know that you're not going to work. You've explained that you don't feel well, so now you write:
I think I'm going to take the day off.
boss (recipient), drinking, email, health, permission, work, 日本語サポート You have some bags of used clothes that you want to donate to a thrift store. You want to know where to put the bags. You see an employee at the front of the store and ask:
Can I drop these off here?
There are lots of different ways to ask for permission to do something:
Can I ___? May I ___? Would it be all right if I ___? Would you mind if I ___?
In the situation above, you don't need to be too polite. So "Can I ___?" is a good choice. Use "Can I ___?" when you want to do something that doesn't cause trouble for the other person. It's also good for asking questions of people that you're close to or on a similar social level with.
To "drop off" something means to leave it in a place. But you only use it for things that you leave on purpose, not by accident. For example:
I need to swing by the office and drop off a few documents. Could you drop this off for me at the post office?
donation, permission, phrasal verb, store You're in a coffee shop. Someone asked to use the chair next to you by asking "Is this seat taken?". You're not using it, so you say:
Go right ahead.
permission, reply, set phrase, strangers 
You are giving a presentation at a conference. You want the audience to ask questions if there's anything they don't understand. Near the beginning of your presentation, you say:
Feel free to ask questions at any point.
conference, permission, questions, speech, 日本語サポート You need to ask your boss an important question, so you go to his office. He's typing something on the computer. You say:
Sorry to interrupt, but can I ask you something quickly?
apology, boss (recipient), interruption, permission, questions, work You're shopping for clothes. You found a pair of pants that look nice, but you want to put them on to see if they fit you. You ask an employee at the store:
Can I try these on?
clothing, permission, phrasal verb, shopping You have a problem with your toilet and want to stay home to wait for a plumber to come and fix it, but today is a work day. You need to ask your boss for permission to stay home, but still continue to work. You call and ask:
Would it be OK if I work from home today?
boss (recipient), home (topic), house, permission, plumber, work 