I don't really want to turn this thread into a thread about Super Mario Bros., but I feel like the "New Super Mario Bros." series doesn't have much difference between each other, while the classic NES trilogy (counting american SMB 2 instead of the Japanese one) and Super Mario World do have more differences.
With the first Super Mario Bros., each world is not themed, like in later games. Pretty much each world functions the same. We get a regular above-ground level, an underwater or underground level (except in the night worlds and last two worlds), a tree level of some sort (except in the last two worlds), and a dungeon, where the boss is always Bowser (technically a regular enemy disguised as Bowser). Worlds 3 and 6 take place at night instead of day, but otherwise, you could swap any levels into other worlds and it'd make no difference. They could have just been levels instead of worlds (not sure if the structure or dungeon levels are what justify them being worlds).
Super Mario Bros. 2 is the first one to have themed worlds (and that game originally wasn't a Mario game). Of course, unlike later games, some of the same themed worlds repeat (there are two desert levels, and two sky worlds). Super Mario Bros. 3 is the first game to use a map, and they no longer repeat the same theme for multiple worlds. Though there are quite a few levels that don't really have anything to do with their respective worlds (Giant World has a few levels without giants, Water World has levels without much water, the first few levels of Sky World take place on the ground, etc.). Many of the later games would reuse many of the same type of worlds (a desert world, a dark world, a snow world, a water world, etc.), even Super Mario Bros. 2 had some of the same basic worlds used in other games. And interestingly, it seems like the second worlds usually have to be desert worlds.
Super Mario Bros. 3 was also the first to have more power-ups than mushroom, flower, and star (not counting the poison mushroom from Japanese Mario 2). It's a shame that none of the new power-ups returned for Super Mario World (I think I've read that Racoon Mario originally was going to be in the game). And that game has less power-ups, with only the cape (which is very similar to Racoon Mario) and power balloon. Though Yoshi is sort of like a power-up, being able to ride him, walk on some things that could hurt Mario or Luigi, and get special powers when eating a certain-colored turtle shell (and the different-colored Yoshis also have special abilities when eating any turtle shell). Though now that I think about it, I think most of the worlds in this game don't follow a real theme, either.
And yet with the recent New Super Mario Bros. series, I feel like the games are all similar to each other (well, I haven't played New Super Mario Bros. U). Aside from the games having their own power-ups (in addition to the mega mushroom and mini mushroom appearing in all the games), they seem to have the same kind of worlds (though as I said earlier, even the classic games had the same themes for various worlds). I don't know why The New Super Mario Bros. 2 needed to have 2 in the title, instead of 3DS (besides, it's the third game). So the first one has Bowser Jr., the second has Jr. and the Koopa Kids, the third one has Koopa kids but no Jr., and I don't know about the WiiU one.
I really enjoy The New Super Mario Bros. series, but at the same time, feel the games are all more-or-less redundant.
As for the Sonic games, Sonic 2, CD, 3, and Sonic and Knuckles are all better than the first one. The first Sonic pretty much suffers "first game syndrome" like the first Super Mario Bros., though it is a lot more cooler. The later games add in funner stuff like the spin-dash. Of course, while Sonic and Knuckles is better visually, I feel like it's too challenging too early, though I know that's because the levels in that game were originally meant to be in Sonic 3. As for the other Genesis-era Sonic games, I feel like Sonic Spinball and Sonic 3D Blast haven't held up well, though I liked them both a lot better when they were new (and it really pains me to say this about Sonic Spinball). And I feel like the Sonic Game Gear games are all just as great (if not less) as the first Sonic Genesis game.