This is probably a silly question, but I just wanted to confirm this. Is there ever a situation where you would need permission to post a link to someone else's site on your website? Or is it always okay to include links to any sites you like?
It's generally OK. It's courteous to let someone know if you're adding them to a sidebar.
Don't link directly to images without permission; that's called hotlinking and it's rude since you're consuming their bandwidth, and they'll have to pay for it.
What do you mean adding them to a sidebar?
As in a blog roll; a list of sites that appears on every post.
It's no small thing to be placed in a sidebar—so a courteous note re: I love your site so much/this particular post so much I've added it to my blogroll/sidebar etc. is a courteous way to let them know they're appreciated and to say thank you.
It's a way of saying "Expect more traffic." If they pay for their bandwidth based upon usage, they can plan for using more bandwidth.
I suppose it would be nice to give them a heads-up anyway.
It's generally OK. It's courteous to let someone know if you're adding them to a sidebar.
Don't link directly to images without permission; that's called hotlinking and it's rude since you're consuming their bandwidth, and they'll have to pay for it.