There are a few general rules concerning the acidity of compounds, but these only give approximations relative to comparable compounds. Even then the real difference in acidity can easily be a few (or more) orders of magnitude.
These are some rules from the top of my head, so don't expect them to be complete, but they're general guidelines.
Negative charges decrease acidity of any remaining acidic hydrogen atoms.
For mineral acids:
1. Halogen acids (HF, HCl, HBr, HI) are all very strong acids (pH -5 and up)
2. Oxoacids (general formula HmXOn, for example sulfuric acid) are weak to very strong acids. Acidity increases along with the number of oxygen atoms.
For organic acids (and any organic compound can be made an acid):
1. The presence of electron withdrawing substituents increases acidity, both through inductive and mesomeric effects (not necessarily together). This is a very general rule, and I'm not inclined to go into detail as there's a lot of ground to cover concerning all possible classes of substituents. Again, more electronegative heteroatoms increases acidity.
2. Hybridization of the carbon atom: more s character increases acidity of hydrogen atoms bonded to that carbon.
Remember these pKa values (for the parent compounds, thus only C and H present): Carboxylic acids, 4.50-5. Alcohols, 16-17. Ketones and aldehydes, 20. Acetylene, 25. Ammonia, 33. Alkenes and aromatic rings: 40-44. Alkanes, 50-60.