The best set of earphones might depend upon your preferences, your goals, your budget, and other consideration, so let me focus on giving you some background and explaining how you can educate yourself and make an informed decision.
If what you care about is sound quality, I recommend taking a look at Head-Fi.org and Hydrogenaudio forums. You can read through dozens and dozens of knowledgeable reviews of headphones there. This buying guide from Head-Fi provides an excellent buying guide for shopping for headphones.
If you care about sound quality, I do not recommend relying on mainstream sources (e.g., Cnet, random web sites, tech magazines, etc.) for headphone reviews. They have extremely poor knowledge about this topic and are often a poor judge of sound quality; I'm often disappointed with their reviews.
There are several different categories of headphones: earbuds, full-sized circumaural hadphones (these go around your ear, but do not rest on the ear itself), full-sized supra-aural headphones (these have pads that rest on the ear), and in-ear monitors. The circumaural and supra-aural headphones can be "open" or "closed". Each of these varieties has different tradeoffs.
Earbuds are small headphones that fit loosely in your outer ear. They are portable, cheap, and widely available, but give the worst sound quality.
Circumaural headphones can give excellent sound quality and are comfortable, but they're large and not so portable.
Supra-aural headphones can give very good sound quality. Opinions vary about their comfort, and they're not so portable.
In-ear monitors go inside your ear canal and form a tight seal. They are basically like earplugs, with a tiny speaker inserted into them. They offer excellent sound quality (in my opinion, the very best sound quality). They offer very good portability. They're also very good for travel (because they block outside noise). However, they tend to be expensive, and some people don't like having something stuck in their ear. Also, they are not so good for walking/running, because a bone-conductance effect causes you to hear a thud every time your foot strikes the ground.
As far as open vs closed (which only applies to the full-sized circumaural/supra-aural variety):
Open headphones don't try to provide any seal. This means that if you use them in a room with others, other people may be able to hear some of what you are hearing. If you're using headphones to avoid bothering others, you might not want open headphones.
Closed headphones provide a bit of a partial seal, so you won't bother others.
Personally, I love in-ear monitors. I love the Etymotics ER-4P; they are an outstanding quality, a reference in this space. Shure, Westone, Ultimate Ears, and others also make very high quality in-ear monitors.
If you care about sound quality, you'll be amazed by the difference in sound quality between your Apple stock earbuds and good in-ear monitors (or really, any quality headphone); the difference is enormous. You'll pay a lot more, but in my opinion, if you can afford it, it's worth it.
If what you care about is that they're cheap, you might want to look at earbuds. If you're looking for medium-priced open supra-aural headphones, Grado has pretty good value (SR-60 or SR-80). For full-sized headphones, Sennheiser is a standard, well-respected brand. But see the buying guide for more specific recommendations.
Since you mentioned you want headphones with a microphone capability, you could look at Etymotic's headset + earphone products, such as the MC3 or HF3; both are advertised as providing support for the iPhone, microphone, and full 3-button remote control. I'm sure there are many other excellent options from other vendors; I mention the Etymotics ones only because I'm a happy customer of their other products.
I'm afraid I don't have any data on durability. All I can tell you is that I've had my Etymotics ER-4P headphones for over a decade now (heavily used: I use them daily), with no problems. You can find price information via the web or at your favorite store.