My father is Italian, his parents were both Italian and came to Scotland from Italy, then to the US.

I was telling him recently how I wanted to visit Italy. He said when he went back to visit about 20 years ago, it was full of crime. Is this true? I'm not sure what part he visited - I could ask him.

Italy is full of petty theft ( I think that was it is called ) - So if you carry something in your car they migt take it - Foreigners are target much more before they usually carry more money and values than locals.
However about the crime rates there are many areas that are free even from small crimes. I live in the US and while here people are more safe from being robbed they are in much more danger to be killed.
This are 2006 data fo the most violent cities in the US:

Wshington DC has 45 violent deaths per 100,000
Detroit - 41.8 per 100,000
Baltimore - 37.7 per 100,000
Atlanta - 34.9 per 100,000
St. Louis - 31.4 per 100,000

Last week the annouced more police in DC because 4 people got shot ( killed ) in one night in 4 different places!

I will try to find some data about Italy but I really think it is at a much safest level.
What is the situation in Scotland ?

I jutt found this
http://www.governo.it/GovernoInforma..._06/index.html
Omicidi in calo in Italia: nel 2006 sono stati in totale 621. Il minimo storico era stata toccato nel 2005 con 601 delitti. Dati che confermano un trend in diminuzione per questo reato che aveva raggiunto il suo picco all'inizio degli anni '90 soprattutto con gli omicidi volontari commessi dalla criminalità organizzata

According to the document above Italy only had 621 homicides in 2006 - It seem very low to me.

I found that in 2005 in the US 16,692 homicides where committed -
Now Italy has about 50 million people while the US 300 million. You do the math

I would say crime levels can be high anywhere in the world. I am sure certain parts of italy have worse crime rates than than others.

Depends what you mean by crime. Corruption, flouting of environmental regulations, illegal building, tax evasion, then sure, Italy has its fair share of evil-doers. And then there's the "M" word, of course.

But crime that will affect the visitor or the ordinary citizen - really no more than in many other developed countries, and quite a bit less than some.

Watch your wallet/handbag on public transport and other crowded places in major cities, and you'll be fine.

Having said that, I live in a sleepy Tuscan seaside village, and when I was swimming in the sea recently, somebody stole my trousers. Whoever it was must have needed them more than I did, as they really weren't a very desirable garment.