For Joe (whether or not he is for real) and anyone else who is interested.
Yes, Geneva’s crime rate is probably higher than nearly most other places in Switzerland.
But yes, it is still very low compared to nearly every city of similar or greater size except perhaps some of east Asia's cities.
The good news is that it appears the situation is getting better just recently. The authorities seemed to have gained more experience in managing the post-Schengen era (not without some pressure from local anti-immigrant political parties).
In particular some zones which saw a sharp increase in crime (such as the zone between the Paquis and the Train Station, and the Wednesday and Saturday Flea Market in Plainpalais) have now managed to revert back somewhat to their previous state by a change in policing structure and, in the case of the Paquis, in a fairly extensive community effort between local residents, businesses, and the police (along with considerable local media publicity) to agree that a more aggressive police presence was needed.
Sadly, a core issue of managing open borders following Schengen is still being resolved. At the moment, many of the former border checkpoints are not manned. So basically, anyone can cross the border at will.
Local cantons bordering France (Geneva as well as Basle which had a major casino heist) have undoubtedly brought the issue up to the Federal authorities who control the border posts. It would seems a simple thing to re-station personnel in the now empty border posts (Schengen permits free immigration of Europeans but does not disallow the checking of documents at the borders).
But there is a uniquely Swiss political situation which is probably delaying (but will ultimately not prevent) re-manning the border posts. It was mainly Swiss Romande (especially Geneva) which supported the referendum to join Schengen. So there may be a perception that any problems which the French border cantons are now suffering was partly of their own doing.
In the meantime, the rise in crime as well as the economic crisis has supported growing support for right wing politics (to the concern of the current liberal administration).
Until the system adjusts and restores itself, it may seem that crime in Geneva is the worst in Switzerland if you are Swiss. But to foreigners, the situation is still far better than the rest of the world’s major cities (unless you are from Japan or, perhaps, Singapore).
If one is concerned, it is worthwhile to talk to the local police or trusted property agents before choosing a place to live (sadly it is hard to find an inexpesive place to live here also). In general, the areas which are generally considered to be less safe are the Paquiz, Jardin Anglais at night + nearby parts of Eau Vives, and perhaps Avanchet. There are some Genevois who refuse to go into these areas after dark (which most foreigners consider to be over cautious).
By the way, if one comes from a place where crime is high, you also should be aware that there is in general a low tolerance for violence here (as in most of Switzerland). So if you do something which is considered normal for defense (or even civil duty) in many places outside Switzerland (for example, you hear a lady scream and a robber is running with a purse, you stick your foot out and trip him, he breaks a finger), you may be considered the criminal (your violent actions will not be deemed justified by the crime being committed).
In general, most would agree that one should not avoid Geneva because of perceptions of crime (most find getting an affordable apartment rental to be a bigger challenge). But with a little research, one can minimize one’s risks.
In any case, it is likely that the situation will gradually improve as the authorities learn more about adjusting to Schengen. Such is the process of Switzerland’s globalization.
Hope this helps and good luck!