Minecraft has definitely gotten popular in the past decade or so since it was released in 2009 / 2010 - it's become one of the most successful games in history in terms of sales and arguably in terms of its influence.
Despite this, I've always felt that the newer versions of MC don't really encapsulate the same atmosphere of the older versions (Beta 1.7.3 and older). Don't get me wrong, they're both great, but in my mind both (before and after The Adventure Update) are completely different beasts and can't really be compared.
More modern Minecraft versions feel more RPG-like in my mind, sacrificing some of the loneliness the Alpha and Beta versions had you feel. There just isn't as much to do in the older versions - so you have to get creative to have fun! In the newer versions though, there seems (could be wrong though) to be a few set tasks that you have to do (like collect food for the constantly-decreasing hunger bar), so you'd usually always have something to do because the game's told you that you have to do it (if that makes any sense)!
ClassiCube is an open-source reimagining of Minecraft Classic 0.30 made for more modern usage, written in C and available on Windows, Mac OS X, Linux, browser and even Android (although it's still in alpha). When you open the game into Singleplayer mode you're thrown straight into a 0.30-style map, with 0.30-style menus and 0.30-style blocks (same textures and block behaviours). This is effectively 0.30 updated for modern operating environments (and without having to depend on ancient versions of Java), with a new level format and massively increased performance.
However, the fun really begins when you venture into the SMP (multiplayer) mode. While some servers are still just 0.30 nostalga servers, many use the new Classic+Hax and Enhanced gamemodes, where many big and small quality-of-life improvements have been bestowed unto us, such as flight, noclip, custom blocks and more.
The largest and most active server is undoubtedly Not Awesome 2 because of its plethora of maps, active community and playerbase, frequent events and powerful building tools / commands.