The first mud we recognize as such came about in the late 1970’s, developed in England by a couple of students at Essex university, Roy Trubshaw and Richard Bartle. According to Bartle,

The very first MUD was written by Roy Trubshaw in MACRO-10 (the machine code for DECsystem-10's). Date-wise, it was Autumn 1978. The game was originally little more than a series of inter-connected locations where you could move and chat. I don't think it was called MUD at that stage, but I'd have to ask Roy to be sure. Roy rewrote it almost immediately, and the next version, also in MACRO-10, was much more sophisticated. This one was definitely called MUD (I still have a printout of it). The database (ie. the rooms, objects, commands etc.) was defined in a separate file, but it could also be added to during play. However, the result was that people added new rooms that were completely out of keeping with the rest of the environment, and, worse, added new commands that removed any spirit of exploration and adventure that the game may have had. In those days, memory was at a premium, and on Essex University's DEC-10 we had something like 50K maximum (36-bit words) to use. The game definition stuff took up too much memory, so Roy decided to ditch it. The program was also becoming unmanageable, as it was written in assembler. Hence, he rewrote everything in BCPL, starting late 1979 and working up to about Easter 1980. The finished product was the heart of the system which many people came to believe was the "original" MUD. In fact, it was version 3.[1]

It’s worth noticing that even in this very early beginning, several of the basic design patterns for muds are established already, and some of the issues that were to plague designers for many years to come were already evident, such as the issues involved with player-contributed content.

Now, this was not the first instance of persistent world online gaming. For one thing, the original MUD was not particularly persistent in nature, and therefore might justifiably not even be called a mud under modern definitions. There were projects on PLATO, the graphical education network in the United States, which had mud-like characteristics.[2] These games were instrumental in inspiring people like John Taylor and Kelton Flinn to go on and found Kesmai and create seminal mud-like games such as Islands of Kesmai. There had also been multiplayer versions of the text adventure variously titled Adventure and Colossal Cave, which went on to become Zork. Bartle says

There's a reference to MUD in an article on Zork in the December 1980 issue of Byte. Interestingly, it also mentions an earlier multi-player version of Zork, but neither I nor Roy were aware of it at the time. I've never found any other references to it, so I don't know how MUD-like it was.

Regardless of whether there were these other projects, the fact remains that most things of substance that has been accomplished in virtual worlds spring from MUD1 and its children. And children did it have! Martin Keegan’s taxonomy of muds, The MUD Tree, shows that it had around a dozen direct descendants, and from those descendants spring all the major code bases in use today.[3] Taken together with the descendants of a few other early endeavors (some of which may well have come before MUD1, such as the efforts of Taylor and Flinn, or SCEPTRE, developed by Alan Klietz, which went on to become Gemstone), these children are the heritage of virtual world design today.  These mud types segment along design principles, not just code branches, and have come to represent basic approaches or design goals; when one speaks of a MUSHlike environment or an LP-style architecture, one means specific design patterns and constellations of features that are typical of these code bases. And if one cannot speak of these things, then one is likely acting in ignorance of some well-known design patterns and is therefore liable to repeat mistakes made years ago.