Rome can receive many more than 12 terrestrial TV stations, as can be seen here:
http://www.otgtv.it/lista.php?code=RM00&posto=Roma . And before DVB-T, those frequencies that are now digital were occupied by more analog stations.
Athens is another city with a very full VHF-UHF dial. There's three national publicly owned stations (ET1, NET, ET3), a national station similar to C-SPAN (Vouli TV), nine national private networks (Mega, ANT1, Alpha, Star, Alter, Macedonia, 902, Tileasty, Skai), two analog terrestrial pay stations (Nova Cinema, Nova Sports), one station in DVB-T (ERT Digital, featuring Cine+, Sport+ and Prisma+ plus Cyprus SAT), 15 local and regional private stations (Channel 9, Kanali 10, Extra, Blue Sky, High Channel, Mad TV, MTV Greece, Sport TV, Local TV, SBC, Shop TV, Tilefos, GTV, Athina TV, DTV), plus four free relays of satellite stations (Euronews, CNN Internatonal, TV5, Cyprus SAT). That's 34 terrestrial stations plus one digital frequency with three new stations. And many of these stations operate on 2-3 frequencies from different transmitter sites, due to the hilly terrain of Athens and the shadowing that comes as a result.
Any problems with picture quality come as a result of two stations interfering with each other on the same frequency (usually overcome by proper rooftop antenna installations, which are very common), or hilly terrain in specific areas blocking a clear signal from reaching the area. Under normal circumstances, stations operating on adjacent frequencies, with full power, from the same transmitter site, operate without any problems whatsoever and without interfering with each other. I never understood why this was such a difficult concept to understand here in the States, when it so clearly can work if done correctly.
In general, both the VHF/UHF and the FM bands in Southern Europe (Greece, Italy, Spain, Turkey, parts of France, etc.) are far, far more crowded than in the North, where government (public) broadcasters also have a more dominant position in the market. In the UK, there are only five analog terrestrial TV stations, two of which are public (BBC). In Ireland, it's 2 out of 4. Similar ratios exist in Scandinavia, Germany, etc. Likewise, with radio, major cities in Italy, Greece, etc. have upwards of 60-70 FM stations operating legally (or mostly legally) while the FM dials in many Northern European cities are quite sparse by comparison, even when comparing them to cities here in the US.
Cable penetration varies by country, and also seems to be higher in most Northern European states... satellite broadcasting is also very widespread throughout Europe, and Europeans seem to have more FTA (free-to-air) satellite TV choices to choose from, so there are many households who receive satellite TV, but without paying a subscription. There are also some countries were pay TV is broadcast over the air, even in an analog form (such as in Greece). Of course, satellite subscription packages also exist in almost every country throughout the continent, and most countries have cable systems as well, while in some others (like Greece) there is not much of a cable TV infrastructure, but IPTV has been growing rapidly in recent years.