I have recently returned to M:TG myself as well!
I played from 1996 to 2000 (roughly from Alliances to Apocalypse, but the bulk of our cards back then consisted of the Ice Age, Mirage, and Tempest blocks), and last October a friend convinced a group of us to try the waters once more for a single afternoon (we used my old card collection, which nostalgia had impeded me from selling). Now there's 14 of us avidly playing again and organizing regular mini-tournaments at a friend's restaurant. It was like giving free samples of liquor at an AA meeting.
The changes to the game surprised many of us; some are explicit in the cards, while others have more to do with the new design philosophies. Here's a quick summary of the main changes the game has undergone (besides two designs changes to the cards themselves) from the 90's that I can remember:
-There's no more mana burn. If you overgenerate mana, it just goes away at the end of the turn.
-The mulligan is now a basic rule of the game (there's even a few cards that mess with mulligans themselves). You can redraw your hand as many times as you want, but with one less card each time (down to zero. I've read some decks that actually make it reasonable to mulligan down to 2 cards to make some strategies work).
-Legendaries are now only player-restricted, so if I play a Tobias Andrion and then you play another, both remain in game. If I play a second one, my previous one is destroyed.
-All creatures now follow a "Race-Class" subtype structure, so the old "Summon Creature" we were used to has given way to stuff like "Creature - Human Warrior" and "Creature - Legendary Naga Wizard Zombie Space Banana". This was followed by "The Great Update", in which older creatures without the new format were revised, so that old copy of Folk of An-Hava is now legally classified as "Creature - Human". This became important with the surge of "tribal mechanics" in the past decade (decks built around the idea of empowering specific types of creatures).
-Damage to multiple creatures blocking a single attacker is now assigned by the active player (ie, the attacker), instead of the other way around.
-A lot of mechanics that previously existed as specific cases have been standardized into keywords. For example, "Creatures damaged by this creature are destroyed", a long-standing staple of Black, is now simply called "Deathtouch", while things like walls changed the "This creature cannot attack" to "Defender".
-Due to changes in design philosophy, some traditional strategies have either become more expensive to play or have fewer options. Chiefly among them are counterspells, discard mechanics, land destruction, and creature removal. For example, while the old Counterspell had a cost of UU, it stopped being reprinted in 8th and now there are either cheaper but specific counterspells, or more expensive general counterspell (the equivalent to the old Counterspell card now costs UU1).
-The game has become significantly more creature-based. I read somewhere that Wizards felt creatures were at a disadvantage in previous edition when compared to instants/sorceries, so they've made the latter more expensive/with more drawbacks when it comes to handling creatures, while considerably bumping the power of the former, to the point that newer creatures outclass almost every similar equivalent from the past.
-Enchantments now have a subtype called "Aura". This word now sums up all the various "Enchant Creature", "Enchant Land", etc.
-There is now a fourth rarity class above Rare, called "Mythic" (the icon is orange). I think it's like 1 Mythic every 10 boosters or so.
-"Expeditions" are extremely rare non-basic lands that get printed from time to time and can show up randomly in any booster, regardless of the set. These are always foil and can fetch prices well above 100 USD. I've heard they show up every 200 boosters, but I'm not sure if this is true.
-Speaking of non-basic lands, they are now ubiquitous, mainly because the game has greatly expanded on the multicoloured realm.
-In that line, colour combinations that used to be taboo are now highly supported. For instance, the Khans of Tarkir set from last year was all about "wedge decks", that's it, decks with two sister colours plus one enemy colour (such as Green-White-Black or Black-Blue-Green).
-Planewalkers were introduced as a new type of permanent. They are extremely powerful cards that have a "Loyalty Counter", which acts as both their individual life total (down to zero and they are destroyed) and a resource you can spend to activate their powers. They usually have 3 powers, some of which increase their loyalty and others which decrease it, often with an "ultimate" superpower that more or less can end a game when played properly. They are not considered creatures, and thus cannot attack or block, but opponents can use their creatures to attack either you or a planewalker you control. Each point of damage removes a loyalty counter.
-The Formats have expanded and got renamed, such as Type 1 now being "Vintage" and Type 2 being "Standard". "Modern" is a new format that allows cards only from 8th Edition forward, while "Commander" (formally EDH, a format where you play a Singleton 100 deck with a legend that works as a commander and has special abilities) has become so popular Wizards even sells pre-made decks for it. M:TG Online made some other formats popular that have now expanded into the physical game, most notably "Pauper", which only allows common cards.
-Cubes have become a very popular way of playing casual M:TG. A cube is basically a custom set of cards you put together and then use as a pool of cards to create random boosters, thus allowing you to play draft with it. The main advantage is that they allow you to create both a fair playing field (as everyone gets to draw randomly from the same pool) and it lets you determine beforehand the style of decks available (for instance, you could make an Urza's Saga cube to play like it was in those days, or a cube that has no flying creatures in it).
Those are the main changes I can remember, but I'm sure I'm missing a lot of stuff.
