Internet Access/Italy

Wi-Fi is widely available in both countries in hotels and cafes. You'll need to read hotel reviews carefully to be sure the places promising Wi-Fi in all areas really do have it in the rooms. Somerimes the signal is really only strong enough in the lobby, or on whichever floor the office is on.

As mentioned in the first reply, internet access is not a problem in either country but service quality may vary from one hotel to the next. You'll have to sign on with a password in each hotel, and in some cases that means signing-in each time you access the internet. I've found that access in Germany is generally a bit easier.

As in many things, in Italy it is quirky. Sometimes you are only allowed to sign in 3 devices per room, sometimes you can sign in as many as you like, but you need a password for each. (This happened to us in Paris, too.) We have had to go to the desk/owner in a few places and suggest rebooting the router. Don't hesitate to do so.

Speeds vary, but we've even been able to stream through a VPN when traveling, although with varying success. All-in-all, you will have access everywhere.

Wi-fi is widely available now, but be aware that most systems are not secure. You will get home after your trip and find lots of spam email. As a smart traveler, make sure you do not use your credit card, or make any transactions over the web while traveling.

To protect myself a little bit, I do not go on sites like my bank or credit card, so I'm not putting in sensitive information, or checking sensitive information while traveling.

I use the internet in Europe to check news on Yahoo, update my facebook and Facetime my kids at home.

Virtually all hotels will have free wifi. The issue is that depending on where the router is located, the signal may not be that great in your room. If wifi is important to you, I suggest asking the reception for a room that has a good signal from the router (the staff usually knows the best rooms for that). Buildings in Italy (or Germany) are not made with plywood or sheetrock. Walls are made with bricks and concrete, and old buildings have particularly thick masonry walls, therefore the signal doesn't go through those walls easily. For example I have a country house that is centuries old with walls that are 2 to 4 feet thick and the only way to get signal for the smartphone is from the balcony.
In addition to free wifi provided by some restaurants/cafe'/bars, some City governments provide Citywide wifi access at specific hotspots throughout the city.
Florence for example has citywide free wifi hotspots. You can use it up to 500Mb a day.
http://www.comune.fi.it/export/sites/retecivica/comune_firenze/wifi.html
The locations of the hot spots is below:
http://opendata.comune.fi.it/open_csv.html?graficocsv=http://opendata.comune.fi.it/od/wifi.csv&titolo=Wifi
Venice has something similar, which I used in 2013. Not sure now. However the signal varies from location to location. It's not in every corner of the city.

As Roberto notes WiFi is generally available at a hotel property but may not be usable in your room for the reasons he outlines. Hotels will generally locate routers in public areas like the reception/lobby area and in sitting areas.

German "star rated" hotels belong to the Hotelstars Union (HOTREC) which covers properties in Austria, Czech Republic, Germany, Hungary, Netherlands, Sweden and Switzerland: http://www.hotelstars.eu/
Internet access in the public areas (e. g. broadband, WIFI) is mandatory in hotels rated at two stars or higher. and Internet access in the room is mandatory in three star and higher hotels. That said, we have had weak or no signals in our room but adequate signal strength in the public areas.

PS I understand the the Italian "star system" uses regional criteria, not a national or international rating system.

I just returned from a trip to Naples and had no problems accessing the Internet there from my hotel laptop or iPhone.

We have had many restaurants, especially bars, offer free internet access. Convenient when taking a break in the evening. We are just checking emails so not overly concerned about security.