Panama  is by and large a peaceful, mellow place despite its undeserved reputation as some sort of danger zone. You’ll likely be safer in Panama City  than you would in any city of comparable size back home. Violent crime against tourists and affluent Panamanians is still so unusual that when it does happen it’s huge news and causes lots of local hand-wringing about the decline of Panamanian society.
Property theft and other kinds of nonviolent crime are the main concern for the haves, and even this is mainly a problem for those who live in the cities, not travelers.
However, violent crime is on the rise. Most of this is gang-on-gang or drug-related violence in areas few travelers visit. Extreme unemployment and poverty make Colón , historically Panama’s second most important city, unsafe for any outsider. There’s an excellent chance of getting mugged if you wander around here. Avoid that city altogether for the foreseeable future.
Even in Panama City, avoid the poorest neighborhoods, such as El Chorrillo and Curundu, and be alert in transitional ones, such as the historic Casco Viejo  area.
Because of reports of robberies at the secluded Madden Dam (on Lago Alajuela), I do not recommend that travelers visit it even in groups. I have also heard the occasional unconfirmed report of robberies in the national parks around Panama City, but this does not yet appear to be a major problem. Just do not hike alone, which is never a good idea anyway.
Rural areas are generally quite safe, but do not leave valuables even in a locked car when going for a hike in remote spots.
As tourism increases, it’s probably inevitable that scams and crimes against tourists will increase as well. More tourists are complaining of thefts from their rooms at both budget and luxury hotels, particularly in Panama City.
In the last few years, hotels around the country have added in-room safes; use them. There are also reports of thefts from beaches while tourists are swimming or surfing. These generally occur at the more popular surfing spots, such as the north side of Bastimentos  in Bocas del Toro . Again, this is not a major problem, at least not yet. Even the “scams” usually amount to being overcharged for a taxi ride or taken to a hotel one is not interested in. Be alert and use common sense when traveling in the relatively more touristed parts of Panama.