Since a PC has a screen and keyboard (as does a terminal) but also has much more computing power, it's easy to use some of this computing power to make the PC computer behave like a text terminal. This is one type of terminal emulation. Another type of terminal emulation is where you set up a real terminal to emulate another brand/model of terminal. To do this you select the emulation you want (called "personality" in Wyse jargon) from the terminal's set-up menu. This section is about the first type of emulation: emulating a terminal on a PC.
Much emulation software is available for use under the MS Windows OS. See Make a non-Linux PC a terminal This can be used to connect a Windows PC to a Linux PC (as a Text-Terminal). Most Linux free software can only emulate a VT100, VT102, or VT100/ANSI. If you find out about any others, let me know. Since most PC's have color monitors while VT100 and VT102 were designed for a monochrome monitor, the emulation usually adds color capabilities (including a choice of colors). Sometimes the emulation is not 100% perfect but this usually causes few problems. For using a Mac computer to emulate a terminal see the mini-howto: Mac-Terminal.
Some have erroneously thought that they could create an emulator at a Linux console (monitor) by setting the environment variable TERM to the type of terminal they would like to emulate. This does not work. The value of TERM only tells an application program what terminal you are using. This way it doesn't need to interactively ask you this question. If you're at a Linux PC monitor (command line interface) it's a terminal of type "Linux" and your can't change this. So you must set TERM to "Linux".
If you set it to something else you are fibbing to application programs. As a result they will incorrectly interpret certain escape sequences from the console resulting in a corrupted interface. Since the Linux console behaves almost like a vt100 terminal, it could still work almost OK if you falsely claimed it was a vt100 (or some other terminal which is something like a vt100). It may seeming work OK most of the time but once in a while will make a mistake when editing or the like.
Dialing programs for making a PPP connection to the Internet don't normally include any terminal emulation. But some other modem dialing programs (such as minicom or seyon) do. Using them one may (for example) dial up public libraries to use their catalogs and indexes, (or even read magazine articles). They are also useful for testing modems. Seyon is only for use with X Window and can emulate Tektronix 4014 terminals.
The communication program Kermit doesn't do terminal emulation as it is merely a semi-transparent pipe between whatever terminal you are on and the remote site you are connected to. Thus if you use kermit on a Linux PC the terminal type will be "Linux". If you have a Wyse60 connected to your PC and run kermit on that, you will appear as a Wyse60 to the remote computer (which may not be able to handle Wyse60 terminals). Minicom emulates a VT102 and if you use it on Wyse60 terminal the Wyse escape sequences will get translated to VT102 escape sequences before the data goes out to the modem. Kermit can't do this.
Emulators exist under DOS such as telix and procomm work just as well. The terminal emulated is often the old VT100, VT102, or ANSI (like VT100).
Xterm (obsolete ??) may be run under X Window which can emulate a VT102, VT220, or Tektronix 4014. There is also an xterm emulation (although there is no physical terminal named "xterm"). If you don't need the Tektronix 4014 emulation (a vector graphics terminal; see Graphics Terminals) you may use eterm. Predecessors to eterm are rxvt and xvt. eterm supports pixmaps.
For non-Latin alphabets, kterm is for Kanji terminal emulation (or for other non-Latin alphabets) while xcin is for Chinese. There is also 9term emulation. This seems to be more than just an emulator as it has a built-in editor and scroll-bars. It was designed for Plan 9, a Unix-like operating system from AT&T.
Unless you are using X Window with a large display, a real terminal is often nicer to use than emulating one. It usually costs less, has better resolution for text, and has no disk drives to make annoying noises.
For the VT series terminals there is a test program: vttest to help determine if a terminal behaves correctly like a vt53, vt100, vt102, vt220, vt320, vt420 etc. There is no documentation but it has menus and is easy to use. To compile it run the configure script and then type "make". It may be downloaded from: http://ibiblio.unc.edu/pub/Linux/utils/console/
The console for a PC Linux system is normally the computer monitor in text mode. It emulates a terminal of type "Linux". There is no way (unless you want to spend weeks rewriting the kernel code) to get it to emulate anything else. Setting the TERM environment variable to type of terminal other than "Linux" will not result in emulating that other terminal. It will only result in a corrupted interface since you have falsely declared (via the TERM variable) that your "terminal" is of a type different from what it actually is. See Don't Use TERM For Emulation
In some cases, the console for a Linux PC is a text-terminal. One may recompile Linux to make a terminal receive most of the messages which normally go to the console. See Make a Serial Terminal the Console.
The "Linux" emulation of the monitor is flexible and has features which go well beyond those of the vt102 terminal which it was intended to emulate. These include the ability to use custom fonts and easily re-map the keyboard. These extra features reside in the console driver software (including the keyboard driver). The console driver only works for the monitor and will not work for a real terminal even if it's being used for the console. Thus the "console driver" is really a "monitor driver". In the early days of Linux one couldn't use a real terminal as the console so "monitor" and "console" were once always the same thing.
The stty commands work for the monitor-console just like it was a real terminal. They are handled by the same terminal driver that is used for real terminals. Bytes headed for the screen first go thru the terminal (tty) driver and then thru the console driver. For the monitor some of the stty commands don't do anything (such as setting the baud rate). You may set the monitor baud rate to any allowed value (such as a slow 300 speed) but the actual speed of putting text on the monitor screen will not actually change. The file /etc/ioctl.save stores stty settings for use only when the console is in single user mode (but you are normally in multiuser-user mode). This is explained (a little) in the init man page.
Many commands exist to utilize the added features provided by the console-monitor driver. Real terminals, which use neither scan codes nor VGA cards, unfortunately can't use these features. To find out more about the console see the Keyboard-and-Console-HOWTO. Also see the various man pages about the console (type "man -k console"). Unfortunately, much of this documentation is outdated.
Emulators often don't work quite right so before purchasing software you should try to throughly check out what you will get.
Unless you want to emulate the standard vt100 (or close to it). There doesn't seem to be much free terminal emulation software available for Linux. The free programs minicom and seyon (only for X Window) can emulate a vt100 (or close to it). Seyon can also emulate a Tektronix 4014 terminal.
The terminal emulator "Procomm" (which is from Dos), can be used on a Linux PC if you run dosemu to emulate Dos. For details see: http://solarflow.dyndns.org/pcplus/.
There's a specialized Linux distribution: Serial Terminal Linux. It will turn a PC to into a minicom-like terminal. It's small (fits on a floppy) and will not let you use the PC for any other purpose (when it's running). See http://members.wri.com/johnnyb/seriallinux/. It will let you have more than one session running (similar to virtual terminals), one for each serial port you have.
TERM (non-free from Century Software) http://www.ecc400.com/censoft/termunix.html can emulate Wyse60, 50; VT 220, 102, 100, 52: TV950, 925, 912; PCTERM; ANSI; IBM3101; ADM-1l; WANG 2110. Block mode is available for IBM and Wyse. It runs on a Linux PC.
Emulators exist which run on non-Linux PCs. They permit you to use a non-Linux-PC as a terminal connected to a Linux-PC. Under DOS there is telix and procomm. Windows comes with "HyperTerminal" (formerly simply called "Terminal" in Windows 3.x and DOS). Competing with this is "HyperTerminal Private Edition" http://www.hilgraeve.com/htpe/index.html which is non-free to business. It can emulate vt-220. Turbosoft's TTWin can emulate over 80 different terminals under Windows. See http://www.ttwin.com/ or http://www.turbosoft.com.au/ (Australia). See also Reflection
For the Mac Computer there is emulation by Carnation Software http://www.carnationsoftware.com/carnation/HT.Carn.Home.html
One place to check terminal emulation products is Shuford's site, but it seems to lists old products (which may still work OK). The fact that most only run under DOS (and not Windows) indicates that this info is dated. See http://www.cs.utk.edu/~shuford/terminal/term_emulator_products.txt.