Well, that is it. I want better roads, more safe roads, better maintained roads to bicyclists so I am looking for bicycle-politized groups or advocate groups around the world. I believe they may have done a lot of pioneering work about bicycling like in the safety -issue. So do not let the word politics stray you, I am also interested in their research and material/projects they may have.
The question is general, I am not limiting this answer to any specific country.
On a global level, there are two different takes on whether helmets should be illegal, or recommended at all, and what effect that has on bicycling in the community.
Personally, I started wearing a helmet when my first kid was born seven years ago, but find the discussion very interesting.
I don't know of any truly worldwide organizations of that type, and doubt any are out there. I believe you'll have an easier time finding a local organization. I believe a local organization is also going to be more effective at achieving the goals you mention.
Bicycle advocacy of getting better infrastructure (roads, paths, lanes, etc) will have to be focused on the government agencies responsible for constructing and maintaining that infrastructure. Laws about bicycles are an important aspect, too. Cities, counties, states, provinces and countries are responsible for roads and laws, not international/worldwide organizations.
For example, I live in California, in a city about 50 miles from San Francisco. There's a local county-wide organization (bicycle coalition) that works with the county-wide government and the governments of many of the cities inside the county. That county bicycle coalition is affiliated with an organization that covers the whole San Francisco bay area and deals primarily with programs that cover that whole area. Then there is a California-wide coalition. And there are several US-wide national organizations, with one (the League of American Bicyclists) that they all seem to work with somewhat.
There are also organizations that advocate for non-automobile ("alternative") transportation, for pedestrians, for public transportation, for less fossil-fuel usage, etc. Some of those are focused specifically on their particular issue, but many include some amount of bicycle advocacy, too.
Well, in many countries there is a nationwide cycling advocacy group, often organized similarly to motoring clubs. In Germany there is the ADFC, the Netherlands have the Fietsersbond, etc.
A international umbrella organization is the European Cyclists'Federation. I don't think there is any global umbrella organization.
These organizations are all part service organizations, offering things like advice, insurance, member newletters, guided tours etc., and part political/advocacy organizations, which lobby politicians, work for better conditions for cyclists, promote environmental measures etc.
Just google, there may well be a similar organization close to you.
Disclaimer: I am an ADFC member.
I think that advocacy organizations absolutely must operate at very local, municipal scales. Why? because every town is different and has its own unique physical, legislative, and cultural landscape. Some places struggle simply with basic acceptance of the concept of a bicycle on the road, others are concerned with expansion of sharrows/lanes/signage/parking dedicated to bikes, others still are implementing bike-sharing systems.
I think in many towns you'll find the following categories of advocacy groups. Some are more active than others, but all of them contribute in some way to better cycling in general. These organizations are the ones that are doing the nitty-gritty work in the towns in which they operate.
I am taking the word "political" somewhat loosely, some of these groups directly interface with governments, others work indirectly by influencing public perception or working towards specific causes which is perhaps even MORE critical to success in the long term than government interaction.
You can also check out http://www.bikecollectives.org/wiki/index.php?title=Main_Page
or http://www.bikecollectives.org/wiki/index.php?title=Community_Bicycle_Organizations
That will show you a list of bike collectives in every country. It's not complete yet, but it's the most up to date resource I've found. You can then email a bike collective near you to get more information about bicycle advocacy in your neighborhood.
In the UK we have the Cyclists Touring Club:
One organisation that used to have a sharp political edge is Carbusters:
Don't forget that the cycle trade has advocacy in the industry. One UK site of note is BikeBiz:
