What types of calls the PCs get sent on depends on what their characters can handle, the department they work for, and the city they are in. But, for some specific examples...
In the Runner's Toolkit "On The Run", KE gets sent to the mall to stop a brewing gang war between the Orks and the Tech-dudes (actual names changed to protect nobody because I can't remember them), and the runners are there when KE shows up. You could use a situation similar to that to help turn the characters from cops to runners.
Drug busts are always fun. Especially if one of the characters has an addiction of some kind. "Um, where did the evidence go?" "*Snort* *Snort* I have no clue, man. But those 2 martians in the land rover might know."
You could have them respond to calls from local saloons to break up bar fights. Nothing stops a couple of drunken unaugmented humans from fighting quicker than a cybered troll with a badge.
Domestic violence is good. Especially in barrens where rednecks might call a place home. "Well, shit - she wouldn't take no for an answer, so I had ta beat her senseles." "Sir, your daughter is only 7." "And if she wants to make it to 8, she better not sneak out looking like an ork hooker again!"
When I lived in the midwest, one of the radio stations had a daily thing on the morning show called "Small Town Crime Wave". The guys would read police calls like:
1. Police responded to a report of a man running nude through the downtown area. When apprehend by police, the man promised he would not run around naked again. However, he informed officers that the voices in his head were telling him he should have sex with a horse.
2. A man called police to report the theft of a large sum of money from inside of his freezer.
3. A MacArthur Drive woman reported at approximately 7:00pm… a carpet was left on her front steps.
You get the idea here. There can be any number and/or type of calls that come in, no matter how stupid they sound.
If none of that gets your motor running, google "cops parody troopers" and watch that.
