Overview of reactions of alkenes

Hydrogen: 
Alkenes react by addition with H2 to give an alkane.  For this reaction to proceed at a reasonable rate, a metal catalyst must be present to activate the H2 toward reaction.  The hydrogen atoms are added to the same side of the double bond (cis addition).

Halogens: 
Alkenes react by addition with halogens (Br2, Cl2) to give dihaloalkanes with the halogen atoms on adjacent carbon atoms.  A single product is formed because this reagent is symmetrical (both groups at BOTH doubly bonded carbons the same).  The diagram shows that the bromines become bonded to adjacent carbons.  It does NOT show that the bromine atoms are added on opposite sides of the double bond.

Concentrated sulfuric acid then water: 
Alkenes react by addition with concentrated sulfuric acid (H2SO4) to give alcohols.  Adding water to the sulfate product formed gives the alcohol.  The H+ from the reagent is a catalyst for the reaction, activating the double bond toward reaction with water.  Two alcohols are formed if the alkene is asymmetric.  The major product is the more substituted alcohol (tertiary favoured over secondary which is in turn favoured over primary).

Diborane followed by alkaline hydrogen peroxide
The borane reacts by addition with the alkene to form an alkyl borane.  The alkyl borane is then oxidised with alkaline hydrogen peroxide to an alcohol.  Two alcohols result from reaction of asymmetric alkenes.  The major product is the least substituted alcohol (primary favoured over secondary which is in turn favoured over tertiary).
 
Ozone followed by dimethyl sulfide:
This reagent cleaves the double bond to two carbonyl compounds.  These are either aldehydes or ketones depending on whether the doubly bonded carbons bear hydrogen.

m-Chloroperbenzoic acid:
This reagent is an oxidant because it is a peroxyacid.  It reacts with alkenes to convert them to epoxides.  The bonds to oxygen are on the same side of the double bond.