I'll make this sticky till it's fixed.
If you have a 64 bit system, and install wine, chromium, or possibly some other programs, you may suddenly find that although pinging by hostname and graphical browsers work, most other things, such as ssh by hostname, and even yum, are suddenly unable to resolve DNS.
This is caused by some packages that are 32 bit only, such as the abovementioned wine and chromium, pull in a package called nss-mdns, but pull in the 32 bit version.
The package rudely overwrites your nsswitch.conf, adding a line to break most things.
One fix is to edit /etc/nsswitch.conf. You will see a line
hosts: files mdns4_minimal [NOTFOUND=return] dns
Put a # in front of the line to comment it out.
Now, things will work again.
Now that yum is working do
yum -y install nss-mdns
This will install the 64 bit version of the package. Once you have the 64 bit version installed, it will probably once again overwrite nsswitch.conf, re-adding the offending line, but that's fine--if you have the 64 bit version it will work.
If for some reason, it doesn't rewrite the file again, as a reader pointed out, be sure to uncomment the line again by removing the # sign.
It is a known bug, so will hopefully be fixed in the near future.