The Mages Guild in Skyrim takes the form of the College of Winterhold, and they’ve got one of the coolest faction bases in the land of Skyrim.
In The Elder Scrolls V: Skyrim, one of the Mage's in the Collage of Winterhold when asked about Necromancy being despised by the Nords says something likeThose Arcanic views vanished along with the Mage's Guild. Mage's GuildTamriel's Mages Guild was dissolved in the beginning of the Fourth Era, directly following the Oblivion Crisis. From one of Skyrim's loading screen tips:The College of Winterhold is an independent organization, and thus wasnot affected by the dissolution of the Mages Guild at the beginning ofthe Fourth Era.Apparently, the dissolution was due to the Oblivion Crisis itself. Common folk blamed the disaster on magic, and the Mage's guild was a simple scapegoat.
Cites a (real) book, The Infernal City, as supporting this conclusion - I admit, I've never read it.Afterward, the Mage's guild splintered into the Synod (one of whom you meet during the Winterhold College questline), and the College of Whispers. Fighter's GuildUnlike the Mage's Guild, the Fighter's guild is actually still around - just not in Skyrim.
From another loading screen:Tamriel's Fighters Guild has no presence in Skyrim. Instead, warriors seeking adventure and kinship may join the Companions, in Whiterun.It's likely that the Guild didn't succeed in extending to Skyrim because, as noted in another answer, the Companions were founded and held cultural significance in Skyrim long before the Fighter's guild existed. If Serana is to be believed, the College of Winterhold is older than the Mages Guild, dating back to the First Era at least.
If you only go by the documents held by the College, then it is approximately the same age as the Guild. Likely, the Mages Guild doesn't have a hold in Skyrim because the College served the same purpose before the Guild could spread that far.The Companions date back to the Merethic Era; the Five Hundred Companions of Ysgramor were an army which played a vital role during the Return. The mead hall Jorrvaskr which you find the Companions inhabiting in Skyrim is made from one of the original longboats of the Five Hundred Companions, and the town of Whiterun was built around it.
In comparison, the Fighters Guild was established in the Second Era, long after the Companions existed and their mead hall was built. There was simply no need for the Guild to extend into Skyrim, when the Companions served the same purpose and got there first.