Various applications are available on the Mac platform for terminal access and file transfer.

Shell access

Terminal

MacOS X comes with two builtin solutions for terminal access which serve most user's needs.

Terminal.app (recommended), located in the /Applications/Utility folder
xterm, as part of the optional X11 package

File transfer

The examples below indicate how to connect using ssh tunneling. This typically means that instead of a real remote host name and the standard ssh port (22), the host name will be localhost and the port will be the one selected during tunnel setup. Some applications do not offer the opportunity to enter port numbers, but they use the standard ssh mechanism under the hood. This is actually a good thing, as they can make full use of customizations in .ssh/config, in particular host aliases. In the example, "carbon" is such an alias, referring to localhost on port 33301.

MacFUSE

Base package for ssh file sharing – you'll need this for the next two apps.
Requires admin privileges to install.

sshfs

Straightforward Finder integration – makes remote files available as network share.
Recommended for most situations.
Requires MacFUSE.
To connect through a tunnel, simply use your host alias as defined in the .ssh/config file.
To disconnect, right-click or control-click, and select "Eject". This is required before sending a laptop to sleep.
Minor drawback: does not recognize public keys – you'll have to type your domain password upon connecting.
Endorsement: LifeHacker

ExpandDrive

Commercial app (approx. $40), very nice Finder integration
Sister product of SftpDrive for Windows

Requires MacFUSE.
Supports public keys
Review via MacResearch

MacFusion

More flashy Finder integration, but requires more verbose configuration, including knowledge of your local port – what's the joy in that? (ed. )
Supports favorites and configurable sleep/wake behavior.
Out of date: The last available version is MacFusion 1.2 Beta 3 — for use with MacFUSE Core 1.1, Jul 16 2007. Works for me - YMMV.
Requires MacFUSE.

Advantage: does recognize public keys
To unmount, right-click or Control-click and select "Eject".

CyberDuck

More old-school FTP and SFTP browser for Mac OS X, including the GUI being overwrought in the wrong places (ed.)
Supports public keys, but goes its own: doesn't know about ssh-agent or known_hosts
Doubles as regular ftp client (who's still using that? - ed., also, Leopard's finder can mount ftp:// links)
Interesting feature: "Synchronize…" (in the Action menu)