depends.... I have done so in Alaska to Mexico and many places in between. For yrs I would take my motorcycle and a bedroll and be gone every weekend somewhere in Rockymtn west.
I have had MUCH more trouble with PEOPLE than animals. (bugs can be a problem...).
I won't explain the trouble since you are frightened, but NEVER place your tent where some drunk coming into a campground can run over you. (including the OWNER of the campground who may NOT have asked their spouse if you paid, BEFORE running over you.)
I avoid campgrounds. Actually I don't feel too safe sleeping in my car or RV, but I really like sleeping in a rumbling semi truck (within reason... 60 nights STRAIGHT can get a little old).
Tent, open air, camper, car, ... all feel the same. I LIKE camping in WY city parks, and at fairgrounds (If I can't be in the WILD). My top spot is a forest service or national park 'hike-in' tent only (tho not required to HAVE a tent).
The YOUNGER you are the better ! (probably better tasting too
)