Mudlet is a modern client which works on PC, Mac, and Linux systems. It uses LUA for scripting and has a very powerful mapping utility.
TinTin++ - TinTin has been around a long, long time, and it's probably the most flexible client I (Savannah) have ever used. It runs on anything *nix, Macs and Windows. (Free) From their webpage:
Program features are support for regular expression enabled triggers, aliases, gags, highlights, substitutions, macros, timers, delayed responses, events, associative arrays, text formatting, searching the scrollback buffer, 64 bit floating point logical and arithmatic expressions, an automapper with a VT100 map display, multiple sessions, loading and parsing of files, execution of command line scripts, running command line programs within the client (such as ssh and sftp) with full scripting capabilities, splitscreen to separate client input and mud output, drawing of VT100 status bars, and tab completion on the scrollback buffer.
zMud - Retired from development, this client was the staple for many of the players here on Dune. The last version is still quite usable, and works like a charm! You are also likely to find many people who can help you set up. (Free 30 day trial)
CMud - The new and improved zMud, CMUD is faster and offers a variety of new 'features'. (Free 30 day trial)
MUSHclient - A powerful client with many scripting languages, active boards, and good support. The client is also freeware, which is a plus. (Freeware)
MudWalker - Last release was around 2005. Some features are: Compact connection windows that use no unnecessary screen space, supports Telnet, MCP, ANSI color, and TWin protocols, full support for extended character sets, including Unicode and Windows encodings, scripting using the Lua programming language, automatic login scripts with support for multiple accounts, etc.
Atlantis - Atlantis is a client specifically designed to aid in playing those type of games. It is designed from the ground up entirely in Cocoa, and integrates with system services — such as the Mac OS X spellchecker — as much as possible.
TinyFugue - TinyFugue is a Unix MUD Client with a minimal interface and incredibly powerful scripting support. It's command line based (no GUI) making it excellent to run on a headless server, or as a background process (see screen utility). A third-party patch is available to add Python scripting language support. Probably not the best choice for someone new to MUDing, excellent for anyone with programming kung-fu.
Irssi is first of all a text-based IRC client for Unix-like systems, but can also run command-line programs such as telnet in the same session. It is script-able with Perl, and is available for Cygwin. In conjunction with BitlBee you may also keep track of messages over other instant messaging protocols with this program.