Belgium has no law regulating it (Dutch link).
In Finland there is no law regulating it.
France has a law to provide free tap water when serving a meal at a restaurant. (see here). Almost all restaurants in France accept to server free water (and free bread).
Germany does not legally mandate free tap water. Restaurant owners are free to decide what drinks to serve and what to charge for them. (German links.)
In Iceland there is no law regulating it, but restaurants provide free water.
In the Netherlands, a 2011 campaign demanded free tap water in restaurants. Those that provide it can be recognized by a sticker on the window. (Dutch links.)
In Russia there is no law requiring restaurants to serve free tap water. (Russian link)
Spain does not mandate it, though restaurants generally provide free water:
Water is frequently served without a specific request, and is normally
charged for--unless it's included in your menu del dia. If you would
like free tap water instead of bottled water, request "agua del grifo"
(water from the tap). However, not all restaurants will offer this and
you may be forced to order bottled water.
In Italy there is no law about it, but the majority of restaurants will serve bottled water by default. Few of them will deny tap water to customers, and few of them only serve tap or filtered water free of charge.
Condition 3. Free Tap Water for Customers
Many premises already offer free tap water. This condition means that all premises have to give customers tap water for free if they ask for it. This helps people to space out their drinks and not become intoxicated quickly, which reduces the risk of crime and disorder occurring.
The tap water you provide should be suitable for drinking and must be provided where reasonably available.
What is meant by “reasonably available” is a question of fact; for example, it would not be reasonable to expect free tap water to be available in premises for which the water supply had temporarily been lost because of a broken mains supply.
(2) Tap water fit for drinking must be provided free of charge on request.
The Middle East
In Israel, by law (in Hebrew), restaurants are required to serve customers chilled water:
Whoever manages or hold a restaurant, weather as an owner or in other way, a restaurant, a food establishment, a coffee house or such a place where food is served, will make it so each costumer is presented with a pitcher of chilled water, without payment.
In New South Wales since 2004:
It is mandatory to have free drinking water available to patrons at all times liquor is sold or supplied in licensed venues.
In Victoria since 2010:
licensed venues that supply alcohol for
consumption on-site are required to provide free drinking water to their
Exemptions may be granted upon request.
In South Australia, the Liquor Licensing Act 1997 does not require it, but in the City of Adelaide there is a goodwill (voluntary) Adelaide Liquor Licensing Accord which covers it.
Licensed premises in Queensland are required by law "to provide drinking water to their patrons for free or at a reasonable cost."
The Liquor Regulation 2002 has been amended to include a requirement for licensees to make drinking water available to patrons free of charge or at a reasonable cost. For example, a glass of tap water should not cost more than a glass of soft drink.
The Northern Territory's Liquor Act does not specify water must be provided.
In Western Australia since 2007:
Section 115A of the Liquor Control Act 1988 (“the Act”) requires that the licensee must ensure that
water suitable for drinking is provided, free of charge, at all times when liquor is sold and supplied
for consumption on the licensed premises. The penalty for non-compliance: in the case of a
licensee - $10 000; and in the case of a manager - $4 000.
Wherever prices of drinking water are unregulated, it is still rare to be charged for tap water at restaurants and bars, though it's common at self-service beverage fountains (e.g. convenience stores).
States requiring free water at all restaurants:
States only requiring free water where alcohol is served:
States with no known regulations: Alabama, Arizona, California, Colorado