Diablo is, at its core, an item hunting game. Once you reach a high enough level, items become the primary way to improve your character. The constant quest to find new cool items and make your toon even more powerful is what makes the Diablo series of games so fun and addictive.
Before mass duping became rampant in Diablo 2, a lot of the best items in the game were Uniques. Some of these Uniques such as the Vampire Gaze had variable stats (6-8% Life Steal, 6-8% Mana Steal, and 15-20% Magic Damage Reduction in this case). This meant that you didn't just want a Vampire Gaze, you wanted a "perfect" Vampire Gaze. But in the end, a lot of the best items were still Uniques. There were some exceptions to this such as dual leech rings or +2 Skill Amulets, although the latter still needed to be better than Mara's Kaleidoscope.
According to Blizzard, things will be different in Diablo 3 as the Uniques (now called Legendaries; note that Set items are also Legendaries) won't be as good as the top rare items. While some people may debate whether this is a good idea, I personally think it is critical to have better item diversity and a better item economy. Everyone in the game wanting and wearing the same items isn't exactly fun. So how will rare items be better than Legendaries? Well, most of them won't be, but due to the random affixes, a small percentage of them will be better, and that will drive the economy for the top-end items.
So what's an Affix? An Affix is either a prefix such as "Brutal" (which gives between +20% and +25% to the Critical Damage attribute) or a suffix such as "of the Lion" (which gives between +1 and +8 to the Attack attribute). Some affixes modify more than one attribute; for example, the "Cruel" prefix modifies Attack (between +10 and +30) and Precision (also between +10 and +30). Every Magical item will have a prefix and/or suffix (for a total of two affixes maximum). Rare items have a minimum of 4 affixes (at least they did in Diablo 2) and a maximum of 6 affixes. In Diablo 3, rare (including crafted) items with 5-6 good affixes should be better than most Legendaries.
In Diablo 2, players often chose to wear rare amulets instead of Unique ones. Those amulets had +2 Skills (of a given class) and other popular attributes such as: All Resists, +Strength, +Dexterity, +Life (especially for PvP), Life Leech, Mana Leech, Magic Find, Faster Cast Rate (for caster classes). If you were playing a Barbarian, you probably wanted a +2 Barb amulet with Dual Leech, ideally some stats (Str/Dex), and some resists, life, or mana. The better the stats, the more the item was "worth", both in terms of in-game trade or black market item sites. In that regards, Diablo 3 will be the same, but hopefully without the black market thanks to the in-game gold and real-money Auction Houses.
I listed some of the attributes that were popular in Diablo 2, but it's hard to know which attributes will be the best in Diablo 3. For example, would you rather have +10 Attack or +10 Precision? The answer will probably depend on your build and spec. One thing that I know from many years of playing World of Warcraft is that Blizzard has done a pretty decent job of balancing the "Haste", "Crit" and "Mastery" attributes in WoW. While one of the three is invariably better for a given spec, the difference isn’t huge and you will always end up with a mix which is not a bad thing.
I suspect that some of the really good attributes in Diablo 2 will remain good in Diablo 3. Let's look at one in particular that was amazing in Diablo 2: Life Steal. In Diablo 2, you could get up to +9% Life Steal on weapons, 6% on amulets, +8% on rings, +8% on circlets (although classes that wanted Life Leech would probably wear Vampire Gaze over a rare circlet), and +3% on gloves (which you rarely did since you could get enough elsewhere and get something better on your gloves). In sharp contrast, in Diablo 3, the Life Steal attribute (with affix names: Vampire, Fiendish, Gruesome, and Exsanguinating) only ranges from 1-3%, and is only available on weapons and Mighty Belts (Barbarian only). That's a huge difference from Diablo 2 where most Barbs would walk around with around 30% Life Steal.
One thing that really surprised me was that Blizzard included (added in Patch 7841) the "DamageVsMonsterType" affixes. The reason this is so surprising (even though Diablo 2 had them) is because Inferno difficulty is supposed to be the same across all Acts. If you can acquire a lot +Undead damage (for example), it seems that you will only farm areas with lots of Undead. This goes against what Blizzard said about making Inferno difficulty even across the board: so that players would not want to farm only certain areas and bosses.
Looking at the Diablo 2 versus Diablo 3 affixes, I noticed a number of differences. Diablo 3 does not have any +All Class Skills attribute (e.g., +2 Barbarian Skills), instead, it has (as did Diablo 2) +1 through +3 of an individual skill (e.g, +3 Rend). These skill affixes are only available on the class specific items (e.g., Mighty Weapons and Might Belts for Barbarians, Hand Crossbows, Quivers, and Cloaks for Demon Hunters, etc). The good news is that your Wizard Staff won't end up with +Barbarian Skills on it. Many of the worthless Diablo 2 skills such as "Stamina Regeneration" and "Light Radius" are gone. Diablo 2 also had some skills that ramped up with level (e.g., "+Armor per Level") which don't yet exist in Diablo 3. In patch 7841, affixes with "proc" effects (a "proc" is an effect that has a small chance to trigger every time you successfully attack; once triggered, the effect usually cannot re-trigger until its "internal cooldown" time has passed) were added: blind, chill, fear, freeze, immobilize, knockback, slow, and stun. The proc affixes are only available on weapons (including off-hands), amulets, and rings, and have between a 0.5% and 5% proc chance. Proc effects did not exist in Diablo 2[Correction Proc did exist] and are probably a replacement for the "charged" effects (allowed any class to cast a given spell with a fixed level, but had a limited number of charges).
One final difference I want to point out between Diablo 2 and Diablo 3 affixes is that the latter has a large number of "Legendary" Affixes. Unfortunately, Legendary items in the beta are currently being worked on so most of them do not have stats in the MPQ game files. The data for anything Legendary is likely to be wrong or incomplete. For example, the "AllStats 8" affix ("of Perfection") has a range of +63 to +71, while the "Legendary AllStats 8" affix only has a range of +30 to +35. I also don't know whether the "Legendary" Affixes are only used for Legendary items. It's impossible to know that from the current MPQ game files.
Part of the fun in Diablo 3 will be figuring out which attributes are the best for your different toons and watching your toons become more powerful as you find better and better loot.
Everything was changed from +skills to +weapon damage; probably to make it easier to balance things out. In D2 when you swapped to your barb with x2 +3 spears to get that extra shout buffs it changed even weak chars... now all the skills (seems like even life leech) will be more skill/rune based which is an interesting concept. I like the variety and if they can keep it balanced it will keep everyone from running FOTM