What is the maximum number of files a file system can contain?

Ext4 has a theoretical limit of 4 billion files, which is restricted by the size of inode number it uses to identify each file (ext4 uses 32-bit inode numbers). However, as John says, ext4 allocates inode tables statically, so the actual limit is set when the filesystem is created.

The df command shows you a count of free inodes on your filesystem:

$ df -i

Filesystem        iused     ifree  %iused  Mounted on
/dev/disk0s3   55253386  66810480    45%   /
/dev/disk1s3   55258045  66805821    45%   /Volumes/Clone

Ext4 also supports an unlimited number of sub-directories per directory, though it may default to a limit of 64,000. This is configurable -- see the ext4 article at Kernel Newbies.

For more information, see The new ext4 filesystem: current status and future plans from the 2007 Linux Symposium.

There isn't one, per se; it depends. When you create an ext4 file system, you decide the size of the inode table, which in turn governs the total number of directories or files the file system can hold at once.

Not Ubuntu, but on Redhat Linux basic commands such as find fail with a 'Too many arguments error' when run against a directory containing 3 million files. ls runs successfully if no parameters are included, but fails with the same error as soon as filter parameters are added.

Assuming reliability of such basic commands is a mandatory requirement I'd suggest that 3 million files is too many.