Bangkok is full of shopping malls and street markets of all types, especially in the Sukhumvit area; see the section for details. Prices can be cheap by Western standards, especially for locally produced items such as clothes, although bargaining is expected and required. Dump a teenager in MBK or Emporium with a few thousand baht and they'll stay occupied for the rest of the week! Most malls tend to have excellent food courts.
Weekend Market: A major attraction on weekends is the gigantic Chatuchak Weekend Market (also a.k.a. JJ Market), in northern Bangkok but easily accessible by Skytrain and Metro. Takes around an hour on the bus from Khao San Road area and has 20,000 stalls selling everything from counterfeit goods, animals, art, furniture and probably anything else you can think of. Definitely worth a visit for the sheer size of it.
Night Market: Hugely popular with tourists & locals alike is the open air Suan Lum Night Bazaar. This is a large and colourful market offering bargains on everything from clothes, bags, crockery to organic foods. There is a large food court with a live band every night. Covered in more detail in the Silom section. Note that as of March of 2007 there is a current worry that the Night Bazaar may be evicted from its premises and replaced by real estate development. The current management of the thriving bazaar, as well as the vendors in its stalls, are resisting eviction, but the owners of the land -- namely the property management company owned by Thailand's king -- is planning the eviction, which may happen as soon as April 2007.
Computer Mall: Pantip Plaza is a multi level computer mall selling everything from branded laptops to cheap VOIP phones and pirated DVDs. A must for any computer & electronics buff.
Bangkok's pharmacies (drugstores) tend to offer a very wide range of (wholly legal and legitimate) medicines and herbal remedies at a fraction of Western prices, including many drugs that would require a doctor's prescription in other countries. Thai pharmacists tend to be exceptionally helpful, and most speak excellent English. There are small, independent pharmacists on almost every corner, and you'll find bigger (and more expensive) chains on the major streets and in shopping centers. Boots is probably the most ubiquitous chain; they're also a reliable source for traveler's toiletries.
Books: B2S on the the 3rd floor of the Central World Plaza is Bangkok's largest bookstore, holding around 30,000 titles (many in English) and large selection of magazines. Japanese chain Kinokuniya also has a large outlet in Siam Paragon (Level 3 South), with a good selection of guidebooks and comics in English.
Clothing: Bangkok is well-known for it's plethora of tailors and high-quality fabric available locally. As a rule of thumb, avoid ANY tailor that you're taken to since many are frequent bribers of tuktuk drivers and others. Generally Sukhumvit-area tailors are western-oriented.