Really it's a question of quality or quantity, and who are the gifts for.
If you want lots of gifts for lots of people, you will have no problem finding a market that sells trinkets and t-shirts all with a Thai theme. Counterfeit goods are also around and cheap.
If you are looking for something more substantial, you can get something that is available in your own country, but is cheaper in Thailand. Genuine designer goods are an example. Try a good shopping mall like Central World, Emporium or Paragon. All the brands are there, and expensive by Thai standards but a fraction of the price you would pay normally.
You can also stay upmarket and Thai by going for genuine Thai silk. Jim Thompson is the best place for that - silk pyjamas might be a good gift for someone. There are a few Jim Thompson shops around Bangkok - have a look at www.jimthompson.com for locations. Warning on the main Surawong store - touts in the area will tell you it is closed/expensive/something to get you to go to their shop instead.