Yes, crime rates are high. but tourism is like a really really really very important thing in Rio? so no, chances of a tourist being victim of armed robbery or other violent crimes are slim, specially in most touristic areas, or areas surrounding international events, where there's a lot of police and surveillance. Even some favelas are now "pacified" and are a very hot spot for safe tourism.
the only crime that one visiting the touristic areas of Rio should be aware of are pickpocketing and small commercial scams (scalpers or service overpricing), but this should be a concern in most touristic or big cities of the world nowadays.
Specially in Rio, there's the concern of making it a very safe place for tourists so there are even police squadrons specialized in supporting foreign tourists. Honestly, as someone working very closely to foreigners in brazil, i can safely say that Rio is one of the safest cities to visit in brazil, and is probably as safe as other major touristic cities in the world as NYC, London or Paris.