According to OICA, Honda's production of cars/LCVs fell from 3.9m to 3.0m, or from 5.9% of world production to 4.5%. That's nearly 1 million units less in one year! Sales continue to fall in many markets for 2010 as well. Honda certainly hasn't chased market share because it hurts profit and can affect resale value of the product. Honda make good, if sometimes conservative cars, therefore they often appeal to an older demographic of customer because of that. The hatchback pictured was designed to break that perception.
So production figures for main countries, starting with '08 production and % of total Honda, followed by same for '09:
The UK had a massive fall but is picking up in 2010. Western factories generally were hit the hardest as the recession bit. Out of all this, Honda will be smaller but still profitable. It doesn't have any alliances so development costs have to be met by the Honda and Acura brands.
To me, this leaves it possibly vulnerable long term. They have to remain a big enough producer to spread R&D over as many units as possible. Certainly for the time being, they are doing fine, albeit with reduced production for the time being.
The bottom line: Honda is solid in emerging markets, which is very important for future production volumes.