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Walking for me is the ultimate free experience, whether it is an urban walk between points in a city or along a coastal path or up a mountain, it brings you close to the landscape at no cost and gives you an opportunity to interact with people, wildlife and the country along the way. It is the best way of getting an insight into the sights, smells and sounds of wherever you are.
I like wandering around supermarkets in foreign countries (free unless you get overtaken by hunger pangs....). I like the juxtaposition of something culturally familiar but (often) completely alien, obviously outdoor markets are more of the same.
In the UK we are lucky so many of our museums and parks etc are free as this isn't always the case.
I will add a caveat to this, however. I enjoy a freebie as much as the next man but often find that the travelling experience for some people seems to be about squeezing maximum experience for minimum cost. This is fine but when visiting countries where poverty (real or relative) is endemic, it seems churlish not to try and redistribute some of the wealth we have invested in our trip. Is paying a local company a little money to educate and inform you whilst providing employment for a resident not a more worthwhile experience (on the whole) than parroting a few phrases from a guidebook about what you've seen and done that day?

Hang out at a local bar, hook up with someone cute and get them to show you around!  ;-) 

When I went to Reykjavik I made extensive use of a website called www.freecitytravel.com.
It only covers Reykjavik and it lists loads of stuff to do for free in the city and surrounding area. There are 4 categories: Museums, Activities, Nightlife, and Free Events - very useful if you are travelling on a tight budget.. Mind you, it's scraping the bottom of the barrel when it includes "drink the free tap water" under Activities, even though it is the purest in the world!

Japan for free – fun and free things to do in Tokyo and Kyoto

1. Free entrance to the observation decks of Tokyo’s tallest towers!
See Mount Fuji on a clear day from the 45th floors of the Tokyo Metropolitain Government Towers, 799 ft above the city streets!
Toei Subway Oedo Line, Tochomae Station, Tokyo Subway Tocho Station, exit 4, or Shinjuku Station
http://www.metro.tokyo.jp/ENGLISH/TMG/observat.htm

2. Free walking tour of the East Garden of the Imperial Palace every Saturday afternoon, 1-3pm, with a local volunteer English-speaking guide. Book your place by emailing info.freewalkingtour@gmail.comMeet at the stand saying Free Walking Tour at Tokyo Station, Marunouchi Central Exit. 
www.freewalkingtour.org

3. Free bicycle hire at the East Garden of the Imperial Palace every Sunday between 10am and 3pm, to ride a car-free route 2 miles long between the Iwaida-bashi Bridge and the Hirakawa-mon Gate of the gardens. Cycle past pine trees, the palace moat, guard towers and fountains and choose from mountain bikes, tandems, racing bikes and even children’s models. Available from the Information Center next to the Babasakimon Imperial Security Police Station (bring ID).
Nijubashi-mae Station, Tokyo Station, Marunouchi exit or Nijubashi Station, exit 2 Chiyoda line 
http://www.tokyobybike.com/2009/08/imperial-palace-cycling-route.html

4. Geek heaven - Sony Showroom
Located on the lower floors of the landmark Sony Building in the Ginza district of Tokyo, the Sony Showroom displays cutting edge audio visual and computer gadgets and trend-setting prototypes for you to play around with.
Ginza Station, Tokyo Metro Marunouchi, Ginza and Hibiya lines exit B9 or Yurakucho Station, JR Yamanote line
http://www.sonybuilding.jp/e/index.html5. Mad about cars? Toyota Auto Salon Amlux 
One of the world’s largest car showrooms. If you have brought your international driving licence, you can test drive any of the 70 cars on display here for a nominal fee.
Ikebukuro Station Yamanote line, East Exit, or Marunouchi, Yurakucho lines, exit 35.
http://www.amlux.jp/english/floorguide/index.html6. Car theme park for petrolheads - Toyota City Showroom at Mega Web
In the futuristic Odaiba district over the Rainbow Bridge and near the giant Ferris Wheel is the Toyota City Showroom that features hybrid models as well as vintage and racing cars, and offers visitors the opportunity to test drive any of the vehicles in the Toyota range for a nominal fee if you have your international driving licence to hand. 
Tokyo Teleport Station, Rinkai Line, or Aomi Station, New Transit Yurikamome line (sit at the very front of the train for great views!).
http://www.megaweb.gr.jp/English7. Beer Tasting – Suntory Musashino Brewery
On Sundays and Mondays in March, and Saturdays and Sundays November – February you can join a tour of the Musashino Brewery to watch how Suntory make their award-winning beer, and then taste some. Tours last 1 hour and are in English. 
Bubaigawara Station, Keio, JR Nanbu line 
http://www.jnto.go.jp/eng/location/sit/tokyo/t009.html8. Fabulous Flea Market - Oedo Antiques Market
On the 1st and 3rd Sundays of each month at the Tokyo International Forum in the Marunouchi district, 9am-4pm. This is Japan’s largest outdoor market with over 250 sellers and thousands of visitors.
Yurakucho Station, JR Yamanote line or Yurakucho line, exit D5 
http://antique-market.jp/eng/index.shtmlFree things to do in Kyoto1. Two Rival Temples - Higashi Hongan-ji and Nishi Hongan-ji 
Conveniently close to Kyoto Station are these two rival temples, the Higashi one of the largest wooden buildings in the world and reopening in October 2009 after major renovation, and the more ornate Nishi designated as a National Treasure. Both are headquarters of rival Buddhist sects.
Kyoto Station, JR, Karasuma, Kintetsu lines
http://www.jnto.go.jp/eng/arrange/attractions/facilities/shrines_temples/83dn3a000000eihj.html2. The Emperor’s Palace and Gardens - Kyoto Imperial Palace, Sento Goshu and Katsura Imperial Villa 
This is the old Imperial Palace where the Emperors of Japan lived for over a thousand years, although this building dates only from the 19th century. You will need to apply online to the Imperial Household for permission to visit and there are guided tours of the palace in English twice a day, at 10 and 2, Monday to Friday. 
If you are visiting between 1st – 10th November 2009 there are special Open Days, 9am-3.30pm, because this is the 20th anniversary of the accession of the Emperor, and you can just turn up. 
There are also tours of the Sento Goshu Gardens next door, at 10 and 2 in English, with the same application process.
Imadegawa Station, Karasuma line
The Gardens of Katsura Imperial Villa are quintessentially Japanese with beautifully manicured trees, elaborately staged viewpoints, ponds, bridges and elegant teahouses in 7 hectares. Again, you need to apply online to the Imperial Household for permission to visit.
JR Kyoto Station, Kyoto Shiei Subway Karasuma line, Hankyu Karasuma Station, Hankyu Kyoto line.http://sankan.kunaicho.go.jp/english3. Japanese arts and crafts - Kyoto Museum of Traditional Crafts 
A complete display of every traditional craft in Japan, such as ceramics and lacquerware, textiles and kimonos, from the days when Kyoto was the imperial capital of the country and home to the Imperial Court. Descriptions of the crafts and the processes used to create them are in English and there is a lovely museum shop too.
Higashiyama Station, Tozai line
http://www.miyakomesse.jp/fureaika/info_english/index_english.html4. Fascinating flea market - Toji Temple Antiques Market
This is held on the 21st of each month, 7am-4pm in the grounds of the Toji Temple, a 15-minute walk from Kyoto Station – look for the tall wooden pagoda tower. Bargain for ceramics, kimonos, chopsticks, books and prints from over a thousand vendors. There is also a smaller antiques market held here on the first Sunday of each month.
Toji Station, Kintetsu train
http://www.kyoto.travel/place_to_go/kyoogokokuji_temple_toji_templ.html

5. Whisky tasting - Suntory Yamazaki Distillery
At Japan’s first whiskey distillery in the Vale of Yamazaki with a great source of really pure water, just outside Kyoto, you can taste the country’s most popular single malt. Guided tours of the distillery take around an hour and are free, 10am-3pm every day except Sundays.
JR Yamazaki Station, JR Kyoto line, Hankyu Oyamazaki Station
http://theyamazaki.jp/en/distillery/guide.html

6. Car theme park for petrolheads - Toyota City Showroom at Mega Web
In the futuristic Odaiba district over the Rainbow Bridge and near the giant Ferris Wheel is the Toyota City Showroom that features hybrid models as well as vintage and racing cars, and offers visitors the opportunity to test drive any of the vehicles in the Toyota range for a nominal fee if you have your international driving licence to hand. 
Tokyo Teleport Station, Rinkai Line, or Aomi Station, New Transit Yurikamome line (sit at the very front of the train for great views!).
http://www.megaweb.gr.jp/English

7. Beer Tasting – Suntory Musashino Brewery
On Sundays and Mondays in March, and Saturdays and Sundays November – February you can join a tour of the Musashino Brewery to watch how Suntory make their award-winning beer, and then taste some. Tours last 1 hour and are in English. 
Bubaigawara Station, Keio, JR Nanbu line 
http://www.jnto.go.jp/eng/location/sit/tokyo/t009.html

8. Fabulous Flea Market - Oedo Antiques Market
On the 1st and 3rd Sundays of each month at the Tokyo International Forum in the Marunouchi district, 9am-4pm. This is Japan’s largest outdoor market with over 250 sellers and thousands of visitors.
Yurakucho Station, JR Yamanote line or Yurakucho line, exit D5 
http://antique-market.jp/eng/index.shtml

I am not very good with links but you can find the whole article on this link: 
http://www.readyclickandgo.com/travel_guides_Japan_for_free.php