There are a lot of things in TF2 I really enjoy so I'll list 2 things.
Characters and their personality- Very rarely will I ever like a character in FPS titles because they tend to be very one dimensional. Games like Bioshock, Borderlands and Team Fortress 2 are some exception that I know of. Despite being a Multiplayer only shooter, TF2 gives each character a personality. The Scout is a headstrong and arrogant 20 something year old from Boston with an ego, the Soldier is a overly patriotic American that hates every country except America, The Demoman is a black, alcoholic, one eyed Scotsman with a love for explosives and Scrumpy, The Medic is a doctor from Stutgard, Germany with a love for medical experimentation and follows a hypocritical oath. Every character in the game, with the exception of Pyro, has a personality and is one of the reasons people still play the game almost a decade after release.
Emphasis on balance- One of the biggest strengths of the game is that balance is constantly in the forefront. Their is no "ultimate loadout" because each class has different strengths and weaknesses. The Engineer can build Sentries, Dispensers, and Teleporters to protect points, provide a constant source of health and ammo and bring players to important area quicker respectively, however, the Engineer himself is a pretty weak in durability and firepower. The Heavy on the other hand, has the most health and the strongest firepower in game ,but, is held back by being the slowest class in the game and is a constant target for Spies and Snipers. The Pyro is the king of close quarter combat with the flamethrower and his/her/its ability to reflect rockets and grenades. The ability to cause afterburn, extinguish teammate on fire and being the best class for spy checks makes the Pyro a great class. However, The class works at its fullest capabilities when ambushing and the lack of range weaponry makes the Pyro weak at range. Each class counteracts each other and some weapons help beat classes that normally would win. The spycicle allows the Spy to survive a Pyro ambush for a few seconds while the Razorback dissuades Spies from backstabbing Snipers.
TF2 is my favorite game due to the effort Valve put into the game over the years. The game has it's fair share of problems I'll admit. The Gunslinger is the bane of every player, Some of the more recent updates were disappointing like End of the Line, some weapons are either too situational for actual use like the Sun-on-a-Stick and the Neon Annihilator or completely idiotic like the Ullapool caber and the Dalokas Bar, The Phlogistinator promotes a soul-crushing and mundane playstyle and Demoknights are almost unbeatable in close range. Despite the flaws, TF2 has given me more fun then I've played before.