To find a MUD you'll likely want to check out sites that are dedicated to aggregating the MUDs which exist today.
These sites come and go. Top MUD Sites, for example, which had been active for over twenty years, is today a zombie, providing links to MUDs both active and dead but never updating. Another site, The MUD Connector, which had been dead for years, only just came alive again in late July, 2023. A third site founded in the late 2000s, MUDStats, went defunct somewhere towards the end of 2022.
Below are some sites you might check out if looking for a MUD.
Reddit MUD - This subreddit is more a forum than a MUD aggregator, but folks either are advertising their MUDs there or are players looking for MUDs, giving games an opportunity to promote themselves.
MUDBytes - Probably the oldest active MUD community online, MUDBytes has forums, code repositories, areas and more, including an extensive list of MUDs. (Whether all the MUDs they list are active is another question...)
Top Mud Sites - While Top Mud Sites is no longer updated, its front page does list the top MUDs voted on by players between the years 2000 and 2022. You should check it out if you're hoping for a more popular world to play in.
The MUD Connector - This newly-resurrected site has a listing of over 600 MUDs, a handful of which were added in July and August of 2023. There's no telling if TMC will stay up for the long haul, but the list of MUDs that are there should be worth checking out.
The following sites appear to be up-to-date with their MUD listings. They are the sites most frequently referred to by players on Reddit when suggesting games to other players—GameScry - A generic gaming aggregator, this site has a section dedicated specifically to MUDs, and it gives players the tools to find the kind of MUD they're looking for, eg. a player vs player MUD with factions or a MUD which uses French as its primary language.
MUDHalla - One of the older MUD sites still in existence, this MUD aggregator regularly pulls back statistics on the MUDs in its catalog, giving the player a chance to see what games are still active. MUDHalla also maintains a separate mud list with fewer listings.
MUDListings.com - Outside of its MUD listings, this site's most interesting feature seems to be its forum aggregator (unfortunately, forum postings appear to have dwindled to just Reddit.)
MudVerse - A site that's been around since at least 2010, MUDVerse, like Top Mud Sites, lists its MUDs in order of the votes they get from players. And unlike Top Mud Sites, MUDVerse is active.
Grapevine - This site does one thing only—list MUDs.
Grim Wheel is a site dedicated to old school text gaming.
Click the links below to go from section to section of this site.
Buildcraft - Articles which discuss the craft of building on Multi-User Dungeons (MUDs).
MUD Forums - Links to offsite forums that concern themselves with all things related to Multi-User Dungeons.
MUD-Dev - Where you can find archives of the former mailing list known as "MUD-Dev", as well as a link to the newest mailing list.
Imaginary Realities - Archives of articles from the now-defunct online magazine Imaginary Realities.
MUD Listings - Websites which list the many text games still in existence.
MUD Clients - Clients which you can use to connect to an active MUD.
Netbooks - A repository of supplements for tabletop roleplaying games.
Miscellaneous - Links that do not fall easily into any other category.
Codebases - The various public codebases in existence today.
Area Archives - Areas for public codebases such as Circle, ROM and Smaug.