Let me preface with: The Auction House is here to stay. And it certainly offers the player an easy way to simply get what they need. However, I have found no real need to buy anything because the drops I get soloing are more than adequate to fuel my progress.
In D2, a level of rarity beyond anything you could expect to find for yourself existed: the runes and runewords. This fueled the duping movement and unofficial Auction Houses everywhere. Now that we have a secure system to acquire runes or ultra-rare items, we don't really need to because exceptionally strong items are growing on trees.
Also, the removal of runewords has also eliminated all use for non-magical items. Now, nobody even picks them up, which is unfortunate to say the least. Additionally, followers cannot be equipped with armors and a full compliment of equipment, less items are being kept by players in general.
Lastly, without levels on each skill, no items can improve a specific skill. One of the most coveted properties for items was their ability to improve skill levels to well beyond their natural maximum.
These issues are a little discouraging, but solutions exist. Firstly, although there are not skill levels, each skill still does something specific. The effects of skills and passive skills should be able to be increased directly by items. This would improve specialization potential and vastly increase the breadth of item effects.
Secondly, it is frustrating to not be rewarded when a legendary item is found and it is less useful than a regular blue (there were garbage rares in D2 to be sure). Legendary items are awesome - a tweak to the power levels of the blues is a simple fix, coupled with an increase in the legendary rarities. They are uniques, yet a ton are for sale right now at the AH.
Along with providing a use for white items (so that they're not simply discarded on sight), I beleive a few of these tweaks are all that is needed to restore a bit of the lust and greed back to item hunting.