I've written previously about how important it is to be drinking high-quality water that is free of the chlorine, chloramine and fluoride - which takes effort, as these chemicals are are added to the tap water of almost every municipality in the country.
There's a number of reasons for this. Chlorine and fluoride have been shown to have a number of adverse effects in the body when consumed in levels commonly found in drinking water. Studies have correlated chlorination of tap water with increased incidence of bladder and rectal cancers.  Chlorine in water has also been implicated in weakened immune system function and triggering allergic responses. 
As troubling as these potential chlorine-related complications may be, it is chlorine and fluoride's effect on gut bacteria that troubles me the most. More and more research continues to come out demonstrating how critical gut flora are in immune function, weight management, digestion and a number of other processes. In light of the research that's come out over the past few years, it's quite reasonable to think that healthy gut flora may be the single biggest determinant in how healthy or unhealthy a given person is.
Chlorine, chloramine and fluoride are added to tap water because they inhibit bacterial growth. Naturally, these chemicals will have the same damaging effect on our gut flora when we drink tap water. (note: brita, pur and other passive home filters do not remove these chemicals)
So you've switched over to drinking exclusively reverse-osmosis filtered water or spring water. Awesome. You should have eliminated your exposure to chlorine and chloramine, right? Maybe not...
Given my concerns around chlorine and chloramine in water, you can imagine that I was quite disturbed to learn that the water we shower in can potentially expose us to even higher levels of chlorine and chloramine than the water we drink. 
Our skin is our body's largest organ and will readily absorb chemicals it comes into contact with - including chlorine and chloramine in shower water. Furthermore - when we take hot showers, chlorine and chloramine will vaporize and be inhaled. 
When we drink chlorinated water, the body is able to process and safely excrete some of the chlorine that was ingested. When we intake chlorine via the skin or inhalation, however, the chemicals go directly into our bloodstream.
Which Filters Help?
Unfortunately, solving the problem is not quite as simple as installing a basic shower filter. Most shower filters on the market are carbon-block filters. While they will reduce levels of chlorine in cold water passing through them, they have minimal effect on chlorine when the water is hot. If you enjoy hot showers like the rest of the western world, you need a better solution.
Other filter types like KDF and brass filters will remove chlorine from the water, but don't have an effect on chloramine. I recommend researching your local water-treatment department and learning which disinfecting chemicals are in your tap water. If your water is chlorinated and never gets treated with chloramine, you will be OK with a KDF or Brass Filter.
More and more municipalities are switching to chloramine treatment (including my own in Berkeley, CA), so odds are you'll need a more complete filtration system.
One option is a whole-house reverse-osmosis filter system. While this is likely the best option, it is also expensive to install and maintain.
The only type of shower-specific filter that removes both chlorine and chloramine from water is a Vitamin C filter. Ascorbic acid (Vitamin C) actively binds to and neutralizes both chlorine and chloramine in water. Vitamin C filters simply run your shower water through a big block of vitamin C. When all of the vitamin C has dissolved (usually 3-5 months), it's time for a new filter.
Surprisingly, there are only two companies currently manufacturing vitamin C shower filters. I'm using a VITASHOWER SF-2000, and while it filters well, the housing is not particularly well-made. I'd recommend having some teflon tape on hand for the install to deal with leak issues. The other option is the hand-held Sonaki Rain, which seems to have less install issues and has a nice bonus of being able to see when the filter needs to be replaced.