There are a number of different weight loss supplements. The most common:
Stimulants - Caffeine, Ephedra, Bitter Orange Extract (synephrine), etc. These increase energy production, adrenaline (epinephrine) production in the body, and as a result increase metabolic function. The main side effects of these are, obviously, increased blood pressure and a "jittery" feeling if you're sensitive. There are no proven long-term effects.
Pyruvate - This works in a very particular way in the body. By loading the body with Pyruvate, the body increases metabolism in a predictable way to utilize the extra pyruvate. It is non-stimulant (i.e., you won't notice an increase in energy). No known side effects.
CLA - Conjugated Lineolic Acid. Scientists aren't sure how this works in the body, but they have shown it to increase metabolic function. No known side effects.
Appetite Suppressants - Some say stimulants have some appetite suppressing properties (personally, they make me hungrier) but there are products that are classified solely as appetite suppressants. The most popular one right now is Hoodia, which is extracted from a Saharan cactus of the same name. The Sans people (ever see "The Gods Must Be Crazy"?) eat this cactus to stave off hunger for several days during long hunts. No known side effects.
StarCaps - Garlic/Papaya Formula. Actress Nikki Haskell came out with a diet pill a few years ago called StarCaps that would let you lose 14 lbs in 14 days. I've seen it work as advertised, HOWEVER - the results are VERY temporary which leads me to assume that it somehow makes you lose massive amounts of water weight or other tissue. It contains a digestive enzyme which may prevent the absorption of nutrients. There isn't much research to show that it has long-term effects, but I'd be wary of taking this.