Without a catalyst, an alkene will react with bromine while benzene will not. Why is this?

The pi-bonds in benzene are delocalised over the entire ring, while in an alkene the pi-bonds are only delocalised over two carbon atoms. This means that benzene has a lower charge denisity than an alkene so benzene doesn't particularly polarise the bromine molecule. So no electrophilic addition between the bromine and benzene will take place.

The larger charge denisty of the alkene will mean that as the bromine molecule approaches the alkene it is polarised, the alkene can then donate its electrons to the positive bromide ion.