|>>|| No. 13789
Depends on what you want to take out and what your tapwater is like to begin with.
A combined carbon and particulate filter can improve the taste, it can take out some nitrates and nitrites which get into tap water as agricultural run-offs into groundwater. They take chlorine out of the water which is meant to be better for your health (but can't take out chloramine as easily, and water companies are highly secretive about what they add in to water so it's hard to find out if you have chlorine or chloramine.)
The other problem with carbon filters is that it's essentially impossible to tell when they're used up, and if you use them for too long they can actually start leeching more chemicals back out into the water.
Water softeners are useful if you live in a hard water area and your kettle scales up very quickly, but it you use soft water for drinking you should think about calcium + magnesium supplements to replace what you would have if you were drinking hard water.
If you're not sure just get a Britta filter and use that for a while.