Master Skins : all characters had their regular skins , but once you reached level 10 ( which was about the equivalent of 25 now ) you would unlock the Master Skin for that character that you could purchase for 10k gold. yeah the downside on that was that once reaching 10 you had to dish out 10k , but that moment felt awesome. having a master skin wasnt something you could just buy out with a credit card , you had to work for it, learn your character and play it a whole lot. when you were facing someone having their master skins, you knew they had put in the time into it and they wouldnt to be taken lightly, of course theres always the exceptions, but there was a certain respect that came out of those. they were earned 
currency : no shards, no gems. just gold. you get gold from finishing quests and games. you then used said gold to either buy characters or their respecting master skins if unlocked.
skins / mounts : all skins ( at the exception of a few that required gold ) were purchased with real money, there was no messing around to buy gems, to then use gems to buy skins. if you liked a skin/mount and decided to buy it, you would get that but always ALL its available colors too, there was no messing around with, ho well, get that one in blue but now you need to buy the red too if you want it, and also need to buy the yellow. simple, to the point, you knew exactly what you were getting with the money, the prices were also fairly reasonable too and quite often if you bought something, you received an extra little freeby for your purchase, usually a mount.
minion lanes : there was no catapults every 3rd wave if you destroyed a fort. they were only provided once you fully opened a lane. which also provided better pushing power for mercs.
forts and keeps : there was actually a 3rd tower, usually beside the fountain.
so you would have your 2 towers at the gate, the fort/keep and then an other tower .
see dear illidan in below video being…gently moved under his enemy’s towers .
you’ll see there is a total of 3 towers + fort/keep
team fights : there wasnt as much of a power creep as we have now, so team fights were lasting usually longer. healers healed more as well. shortly after hots 2.0 , ALL healers received a 10% debuff on all their shields and healing abilities.
Specialists : soon after 2.0 . there was something nicknamed by some as the “war on specialists” . essentially , that role was top be wiped clean and all heroes who were on that role got moved to assassins at the exception of abathur who got moved to a support. specialists were known a “unconventional” characters which made sense given their nature. azmodan has better pushing power when pushing 2 lanes at once. zagara’s creep was her true power since it provided her team with an awesome visibility on the map, it was also using mana but had much larger radius and shorter cooldown, meaning she could creep much more effectively. nazeebo’s gargatuan could actually be controlled ( very similarly to kerrigan’s ultralisk) . sylvanas’ AA or skill would stun towers so it would make her a scary character if he assaulted one of your lanes unprotected.
tower ammo : towers actually had ammo ( which would replish on its own ) but pushing proprely and constantly against an enemy lane meant that you would end up depleting their ammo for about 30 seconds, which you could use to push safely. fighting lane had a much bigger impact then rather than now since losing a fight in lane doesnt mean much , yeah enemy gets a shot or two at the tower…no big deal, but then , it mean he would likely be able to take down a full tower if not both depending on how much pressure they managed to put.
garden of terror : sure the aesthetics of new one is nice…but the original one was awesome because you were gatering skulls and then you would become the terror, similar to how you become a dragon knight ! you had 3 skills, dash , which boosted your walk speed for maybe 5 seconds. putting a plant down which disabled all enemy structures and finaly a polymorph flower, enemies cought in it would be transformed into a plant for about 1-2 seconds. also depending on the need , you could just go ahead and engage the enemy team with it and sometimes you had both team with enough seeds and you ended up with 2 giants flower monsters battling each other with their team supporting them.
maps : all maps were always on rotation . none of that " we dont want to overwhelm new players so we will only have a few maps in at a time…" . nope ! all maps ! , sure we didnt had as much then as we do now but there was no restrictions on that either.
4+ talents on character tiers : before 2.0. some characters actually had 4 talents per tier ! sure 3 was the norm, but some characters actually had 4 and sometimes 5 ! ( raynor is an example ) . sure not every talents was picked often, but what it provided was a nice utility talents that if you ever needed it it was there. who cared if that talent was useful only 8% of your matches. for the time you actually needed it , it was there and it rocked !
game length : currently the target is a bout 15 minutes. before it was about 20-30 . i was still happy because it was still shorter then a LoL game when i use to play lol .
more original talents : some characters ( like valla , tyrande , tyrael ) had skills were they could activate and each of their AA would be significantly buffed , at the cost of mana. usually using them would end up you going back at teh nexus for a few seconds but it had the potential to win fights. zagara had a nice particulatiry with her nydus at level 20, when coming out of the nydus, she would release 6 broodlings. that would push with the minions in that lane. ( effect had a separate 25 seconds cooldown or something. ) . kerrigan had Zerglings coming out of her W . diablo’s fire stomp could actually be upgraded to be almost screen wide and wasnt a frontal wave but a 8 directional fire wave. the damage wasnt as strong on that but was a nice poking tool and specially a nice scouting tools for camps, if you had suspicions enemies were camping, use fire stomp and see what the fire reveals. more healers had ways to repair structures , so the whole runnig out of ammo was also fixed by that. Thralls sundering was an absolute awesomness ! that thing traveled the ENTIRE MAP at level 20 ! it was such a feeling of being a total bad@$$ of doing this.
like this !
Stealth: instead of that outlines we have on them, they were fully cloacked but had a reflective shimmer on it. it was never that hard to see and many players just complained about they way they complained about tracer. they were just the complain flavor of the moment.
im sure there would be much more we could cover but those are some of the main elements i remember about it 
overall , thats the period where i had the most fun with the game by a long shot, do i still have fun now ? sure , but the game isnt as fun as it use to be unfortunately