One of the best ways to experience Amsterdam is by bicycle, it's a very bicycle friendly city. A few rental places provide a repair kit or even road service to fix a flat---the chances of getting a flat are not remote in Amsterdam. Never leave your bicycle unattended or unattached to something. Simply everyone has had a bike stolen, it's a common headache. So much so, that if your bike is stolen, most often you will not be held liable. If you still have the keys, you'll get another bike immediately. Still it is a hassle.

If paying by cash, they'll usually require a drivers license or passport be left behind, plus a deposit, typically € 23,-. Credit cards make it simple. Special rates can be had for weekly and longer term rentals...the longer you rent, the cheaper it gets. Ask.

Frederic
Brouwersgracht 78
The best bike rental place in town, the best rates. In addition to the standard no-speed Dutch bike, at additional cost they also offer 3 speed and mountain bikes---neither of which you'll need in flat Holland. Stick with the typical Dutch clunker, they look like crap, but are as strong as tanks and you'll still glide for blocks. They're very friendly, and provide great personal service. If you're lucky you may even meet jovial Frederic himself. Beware of his mechanic though, to call him "grumpy" would be an understatement; you can't miss him, he bears a striking resemblence to crazy Van Gogh.€ 10.00/day for the standard clunker (Price drops to € 8/day for more than three days). Weekly rates are 
€ 40,- or about $ 35US. Locks, bike bags, road service and a repair kit are all included. A great self-published guidebook, very good maps and bicycle tour info is also available.

Frederic now offers several lovely rooms, at great rates, in a great location. Recommended

Bulldog
Oudezijds Voorburgwal, Red Light District. 
Tourist bikes with placards attached advertising where you got them that shout, "TOURIST!" About € 5.70/day, if you're desperate.

Macbike
Marnixstraat 220
Theft insurance is additional. About € 9.00/day
Weekly rate is € 27,50.

Rent-A-Bike-Damstraat
Pieterjacobszdwarsstraat 11
Located in a little alley off Dam Square, the usual € 7.00. Weekly rate is € 31.00-

Yellow Bike Tours
Yellow Bike offers several reasonably priced guided bicycle tours through the city, the countryside, etc. Typically the tours last several hours and do not include the price of lunch although a picturesque lunch stop is included. If you're not shy about being herded around in largish groups on ghastly yellow bikes, in matching ghastly yellow rain jackets (in the likely event of rain), with uniformed guides, you'll love this. Prices for tours are in the neighbourhood of € 17.00

Cycletours Holland
Organised bicycle tours throughout Holland. Longer and more strenuous...a degree of fitness is required.

Canal Bike
Another great way to see the city is from the canals. Rent a canal bike, one of those little peddly boats that can seat as many as 4 persons! You can rent one at any one of 4 mooring areas and leave it at any other. Pull up at a canal side cafe and have a beer! Locations at the kiosks near the Rijsmuseum, Leidseplein, Anne Frank Huis, Keizersgracht/Leidsestraat. Rates are 1-2 persons € 6.00 plus small deposit.