These are what we call the 'YMMV items.' Things that some people find in this work. We call them 'your mileage might vary' because not everyone sees these things in the same way. This starts discussions in the trope lists, a thing we don't want. Please use the discussion page if you'd like to discuss any of these items.
Anvilicious: When they have a point to make, they're not subtle about it. Notable examples include "The Last Resort," "In the City," "Get Over It," and at least a third of Long Road Out of Eden.
Awesome Music: "Hotel California" is considered a rock & roll classic. They've got a lot of other good songs too that are classic rock radio staples.
Not to mention good songs that aren't classic rock radio staples, like "Too Many Hands" and "Teenage Jail".
Broken Base: Particularly with Don Felder's 2008 booknote Suppressed for a long time by a lawsuit, which gives it a stamp of authenticity in some eyes and a 2013 television documentary, fans get divided over whether Henley and Frey are really that big of assholes or whether they needed to do the things they did to stay successful.
There's also the relatively minor (in comparison) matter of Bernie Leadon country rock Eagles vs Felder and Joe Walsh rock rock Eagles.
Critical Dissonance: One of the most popular rock bands of all time, but many critics consider The Eagles "corporate rock" at its worst. On the other hand, Hotel California is the one album that most critics acknowledge as a masterpiece.
Through the tribute album Common Thread, Travis Tritt and Clint Black have made their covers of "Take It Easy" and "Desperado," respectively, almost as famous as the originals if not moreso.
"Take It Easy" is itself originally a Jackson Browne song, though Frey co-wrote it. Also subverted in that their version was released a year before Browne's.
"Please Come Home for Christmas" was first recorded by Charles Brown.
"How Long" is a cover of a J.D. Souther song.
"Ol' 55" was originally written and recorded by Tom Waits.
"Seven Bridges Road," the last single from the band in their prime, was originally written and performed by alt-country artist Steve Young.
Couple of curious examples: "In The City" and "Love Will Keep Us Alive". The first was originally a Joe Walsh solo track (written for The Warriors), and the second was for a stillborn project involving Timothy B. Schmidt in the late 80's. Both were released later on Eagles albums, and are much more well known as Eagles songs. As far as Walsh, "Life's Been Good," "Rocky Mountain Way," and "Funk #49" have been heavily played in Eagles live sets.
In the other direction, their song Desperado, as covered by The Carpenters.
Ensemble Darkhorse: Glenn Frey put the band together and was the de-facto leader in the early years. Early concerts and singles had him as the lead singer more often than anyone else. Bernie Leadon, the other guitarist, was also an Alpha Male (actually, all seven past&present band members were/are, for some extent) and there was a lot of tension between those two because Leadon was, in a way, rivalling him in taking the reigns. Guess who would eventually become the most famous band member, the most often lead singer and the most successful solo artist? Don Henley, the drummer! He'd sing a couple of songs and write the odd lyric, then gain more and more prominence and by the mid-70's he'd be the one the audience and the media wanted. He still let Glenn run the show, so it was more like a 'dual dictatorship', which by the way resulted, one way or another, in the bitter retirement (voluntary or forced) of three band members and several people in the crew.
In that case, Henley's more of a Breakout Character, as he was eventually relocated to the front, and that's where he is now at least in terms of singing. Ensemble Darkhorse would suit Randy Meisner better: he was 'just' a bassist and backing vocalist for most of their early hits, until they released "Take It to the Limit", which he sang and co-wrote, and it become their first No. 1 hit and one of their most popular numbers on stage, with a guaranteed standing ovation when he hit the high note near the end. His shyness and self-effacing attitude to it only made his whole persona much more appealing to the audience, and even his bandmates encouragednote In the sense that Glenn Frey told him if he wasn't going to do it, he could just go ahead and quit. One day, he did. him to sing that song as it was such a highlight of their shows.
Everyone Is Satan in Hell: "Hotel California" is the center of several rumors which claim it is actually about Anton LaVey, the Church of Satan, or devil worship in general.
It's the Same, Now It Sucks: Their live act has been criticized for sounding exactly the same as on their albums. Owning one of their live albums is superfluous.
Sophomore Slump: Desperado struggled hard compared to their first album, arguably saddled by the concept nature of it. Additionally, the two singles ("Tequila Sunrise" and "Outlaw Man") flopped. The title track, never released as a single, would go on to be Vindicated by History and became a future live staple and country standard. The album would only make gold and platinum due to "halo" sales after other more successful albums were released. The band would ultimately go in a new direction with On The Border, bringing in a new producer and guitarist.
Tough Act to Follow: While The Long Run spawned some of the band's biggest hits, it's not as fondly regarded as Hotel California.