How to customise the activities tab listing
You can't realy customise the main activities tab. However there are several other options to create other tabs which show activities which do allow more customisation.


Activity Tabs extension written by me, this offers a reasonably easy way to add tab(s) with filtered lists of activities and allows you to choose which fields (inc. custom) you want displayed.
Data Processor extension this is very flexible/powerful, but a bit more of a learning curve (well worth it!)
Extended Reports extension - I've not used this but I believe it allows its reports to be embedded as tabs on a contact record.