After moving over my test blog to the new server, I noticed that the Admin Dashboard (with tons of unnecessary feeds) wasn't displaying. It shows just a blank page.

Apache error log had a very interesting message:
Allowed memory size of 8388608 bytes exhausted (tried to allocate 0 bytes)

The solution is simple.
1. Increase memory_limit in php.ini to a higher value. I have set it to 64MB:
memory_limit = 64M

2. Restart the Apache HTTP Server. On linux that would be:
service httpd restart

Note: The same technique can be used to increase maximum allocated memory for any php scripts.

An even better solution is to replace it with WordPress Dashboard hack.