1) Combustion reactions. In my opinion, they're the easiest in terms of figuring out the products, because the products are always the same! Any combustion reaction will result in the formation of #CO_2# and #H_2O#. An example is the combustion of propane:
#C_3H_8(g) + 5O_2 (g) → 3O_2(g) +4H_2O (g)#
2) Synthesis/Composition Reactions: This reaction is where 2 simple substances come together to form a more complicated one. Typically, you want to look at the charges of the ions of the 2 reactants, and use those to figure out the resulting compound. An excellent example is the formation of water from hydrogen & oxygen gas:
#2H_2(g) +O_2(g) →2H_2O (l)#
3) Decomposition Reactions: This reaction is where 1 complicated compound breaks apart to form 2 simpler substances. Decomp reactions have 6 sub-categories that can help you predict the products. I won't go into these categories since my own chem class didn't cover them, and I probs wouldn't explain them well, but I'll leave this link that goes over them: http://eppe.tripod.com/reaction.htm
4) Single Displacement Reactions: This reaction happens when one element trades places with another element in a compound. An example of this is: #Zn(s)+2HCl(aq)→ZnCl_2(aq)+H_2(g)# With these, make sure that the element that's being switched is switching with an element of the same charge. So like in the example, the Zn is switching with the Hydrogen, because both are cations.
5) Double Displacement Reactions: This reaction happens when the cations and anions of both reactants trade places with one another. An example is: #NaCl+KBr→NaBr+KCl#
6) Acid-Base Reactions: These are actually a sub-set of Double Displacement Reactions, but they're super important to know because you can always predict the products. When an acid and a base react, they always form water and some ionic salt. An example is: #HCl(aq)+NaOH(aq)→H_2O(l)+NaCl(aq)#. In this case, the ionic salt would be sodium chloride (table salt).
Citations: 10th grade chem notes and http://misterguch.brinkster.net/6typesofchemicalrxn.html