Crime should be a dynamic feature in the game. But I think it's time we go beyond the red dead redemption model where you're like "ooh, there's a crime, can I be arsed to go and help?" Crime is in reality something that makes people feel uncomfortable, and I'd like to see the player as being at risk of victimization as well. A few ideas:
1. Characters who are famous are more likely to be attacked, or will struggle to stay hidden.
2. Characters with rare, illegal or valuable items are more likely to be targeted and robbed of them. (say if you fire your railgun, people will know you've got it, and try and steal it, this will put an extra challenge onto players to be tactical about what gear they use and when). This could be a lot of fun if multiplayer opens up and will solve any "ultimate weapon" dilemmas.
3. Police and gang members will shake you down if you are vulnerable. (it's called capitalism baby).
4. Trading illegal goods, or spending stolen money will increase your visibility online (digital footprint or something) and will make it easier for corporates, gangs and maybe even the authorities (meh) to locate you. (this will encourage players to use netrunning chops, or tech).
5. You can always have the choice to fight your way out - (keep trauma team's number at the ready though....)