I've lived in the Tampa Bay area (Temple Terrace, St. Pete, Westchase) for about 4 years. I'm a young professional who moved from Michigan.
Temple Terrace was, bar none, the sketchiest area in which I lived. Someone attempted to pop a window of my then boyfriend's car to steal a crappy GPS while parked at our apartment complex. St. Pete was relatively OK when we lived there in 2009/2010, but has since gone downhill. A crime map will paint the picture for you. Lots of car theft.
What surprises me, however, is the amount of criminal activity in downtown Tampa/SoHo. I've had my wallet stolen out of my purse while it was resting on a barstool 2 feet from our table at Drynk. My co-worker's condo was broken into and cleaned out over Thanksgiving weekend. She lives in Palma Ceia, just a few blocks off of Bayshore. There was a UT student robbed and killed in downtown Tampa late at night. Lastly, I've had my car vandalized while parked at a friend's house off of Westshore/Bay to Bay. I am shocked that this is still a sought after area to purchase a home.
I've never had any problems in Ybor, although bar hopping late on a Friday or Saturday night might rub some the wrong way. There is gang violence, and shootings outside of clubs. Perhaps this area is turning around some. There is a notable increase in police patrol in this area, especially during the weekends.
We live in Westchase/Citrus Park area now, and it is very safe. Carrolwood is relatively safe as well. Harbour Island and Davis Island are other good choices, and a little pricier.
In short, Tampa Bay is a large city, and there's going to be crime everywhere. I think what is more notable than the amount of blatant criminal activity (e.g. theft, murders, etc) is the amount of fraud. This area is filled with dubious characters, who want to take advantage of naive, unknowing people who make bad choices or are too trusting. Even bartenders and waiters will try to make a quick buck, by illegitimately hiking your tab (drunk people don't know the difference), or apartment complexes who charge bogus damage fees.
The worst area you're likely to encounter is gonna be the outskirts of Ybor City. If you drive to Ybor, park in one of the parking garages. They're pretty close to the center and well-maintained. Your other option will be along one of the side streets (at night), say 8th or 9th Ave, and you could encounter some people who are trying to make trouble. Lots of homeless people in and around Ybor. Just ignore them. Don't go walking around alone at night unless you're on the main strip (and even then be careful) - common sense. Be *especially* careful during Guavaween and the Gasparilla night parade!!
As far as getting out of Ybor, drive carefully and try not to get lost. Some of the gas stations, convenience stores and fast food joints (around this area of 275) are really ghetto, and not nice places to stop and ask for directions late at night.
As in most cities, there are parts of Tampa where life is harsh for the residents and tourists need not go. Mind you, I can't recall a single attack on a lost tourist in one of Tampa's "bad" neighborhoods, but there's not much for visitors to see there, anyway.
East Central Tampa is the most neglected part of town and the primary area to avoid. There are tourist destinations right along its edges, so pay attention.
Roughly, East Central is a large rectangle bordered by I-275 on the west, Busch Blvd. on the north, 50th St. (which turns into 56th St.) on the east, and I-4 on the south (see map). Even though the northern edge is across the street from Busch Gardens and the southern edge is across the interstate from downtown and Ybor, those destinations are actually pretty safe.
One more tip on Ybor: you don't want to wander south of 7th Ave. or cross 22nd St. just east of the Columbia Restaurant as the neighborhood gets non-friendly very quickly in those directions.
Like I said, though, if you find yourself driving through these areas, you'll be fine, especially during the day. Sometimes it's good to see how the other side lives.
As with any major city, we have our 'bad' areas. You'll know them when you see them So do what you can to avoid them. Also, the lightning can be pretty wicked, depending on what time of year you're here. Summer mostly, though, is the worst.
Unfortunately there are plenty of neighborhoods to avoid in Tampa. The area just west of Bruce B. Downs and just north of Fowler is not a very pleasant place to be, and I wouldn't be caught hanging around the University Mall parking lot after dark if I were you. Just north of downtown on Florida Ave. is not the most desireable locale, and Nebraska avenue is very well-known to the locals for its 'night-life', if you catch my drift. Just be aware of your surroundings and you should be fine.
Like most towns, we have a few questionable neighborhoods. They are not around every corner as is suggested eleswhere. If you are in Ybor City, then you will want to be careful leaving the area or you could get lost. Otherwise, most places you will want to see are easy to access and safe.
If you get off the highway to ask directions, and the neighborhood looks bad, it is. Only ask for directions at well lit gas stations or restaurants. There are a couple places near the highway where you should just not go, as in every major city.