Famicom and 360: The Famicom launched with games like Donkey Kong and Popeye. By the time the NES, which was the same hardware repackaged for a western audience, launched it had true scrolling games like Super Mario Bros. A few more years and it had SMB3, which made the original game seem like another generation behind, and by the end it had Kirby, which could almost be mistaken for a 16-bit game.
The 360's launch games were pretty unimpressive graphically even at the time. Condemned was the game with the best graphics in 2005, and with games like RE4 on the Gamecube, God of War on the PS2, and Far Cry on the OG XBox, the 360's graphics were pretty unappealing at launch. Then came games like Oblivion and Advanced Warfighter, which started to show the difference between the 6th and 7th gens. A year after it launched came Gears of War, which finally showed off what that generation of consoles could do. Somehow the 360 was able to keep pace with the PS3 throughout the generation, getting all of the Call of Duty games. Even though Oblivion seemed cutting edge when it launched and Skyrim was leagues above it, Skyrim actually seemed somewhat outdated at launch in terms of visuals because of how far graphics had come. Halo 4 looked so good it was hard to believe it wasn't an 8th-gen game, and the 360 was somehow able to run Crysis 3. Not well, but it ran it. No one who saw COD 2 and Kameo at the 360's launch could have imagined the system could run games like Halo 4, Gears of War 3, Battlefield 3, ect.
For least difference between launch and end of life-cycle graphics I'll have to go with the Gamecube and Dreamcast. The Dreamcast suffered from a pretty short lifespan, so there wasn't much time for graphics to improve and we'll never know how well the system could have kept up with the Xbox and the Gamecube if it had truly competed with them. Shenmue 1 and 2 are very advanced for their time, but when a system launches with Soul Caliber there's not that much room for improvement.
The Gamecube's launch titles were really good and held up extremely well. Rogue Leader still looks good to this day and while Rebel Leader does look better, it's not that much better and still uses much of the exact same assets. Other games at or near launch included Luigi's Mansion, Melee, and Wave Race Blue Storm, all of which were still graphical showcases for the system in its final years. Metroid Prime, REMake, Prime 2, and RE4 all set new benchmarks for graphics, but they weren't a giant improvement over the launch games like you usually see for most systems. I'd actually say the Wii had a bigger difference between its best-looking games and its launch games than the Gamecube did. Mario Galaxy, Red Steel 2, Conduit 2, Prime 3 and Other M, The Last Story, Skyward Sword, and Sonic Colors have a larger improvement over Twilight Princess, Red Steel, and Wii Sports than Prime 2, RE4, and Rebel Strike have over Rogue Leader, Luigi's Mansion, and Pikmin.