Windows 7 Service Details
The DNS Client service is not needed to connect to the internet. It is used for DNS client lookup caching. However, browsers already have DNS caching built into them. Some people have mentioned that this will slow down your browsing experience as you will have to re-retrieve DNS entries for all web requests, but I find that 2 levels of caching the same data is a bit silly, as the browsers can manage this on their own. You can up your DNS browser cache from within firefox (and probably IE), or use an extension such as FasterFox which ups it by default (if memory serves).
The DNS Client service (dnscache) caches Domain Name System (DNS) names and registers the full computer name for this computer. If the service is stopped, DNS names will continue to be resolved. However, the results of DNS name queries will not be cached and the computer's name will not be registered. If the service is disabled, any services that explicitly depend on it will fail to start.
Consequences of Stopping:
If disabled DNS names will continue to be resolved but they won't be cached. Your internet will continue to work just fine. Can slow down browsing, hypothetically, but I have seen no difference in network speeds. Also some ipconfig commands will complain about errors (as there is no cache to clear)
All services listed in 'Required For' will be unable to function