I own the Denon D2000 after a whole slew of other headphones. They are by far the best of all I tried. If you are listening to Techno/Trance, like I do exclusively with headphone usage, they are the best headphones you will ever own for this type of music.
Some important notes:
1. The headphones do have a loose fit. I solve this when I lay down by simply tying a bandana around my head, which I slot into the headphones between the headband and earcups. It's a perfect fit, and keeps them on your head just fine when you lay down.
2. These headphones are not what I consider a true closed headphone, in the sense that they do not prevent sound from leaking in, and they also leak out a bit. I can even hear my fridge when it's on in the next room, a fan, whatever when I'm listening.
3. The D2000 sound way, way better - IMHO - than the D5000. They sound much quicker, better rounded, with cleaner and tighter bass. The D5000 was pretty, but had very recessed midrange to the point the singer sounded like she was in the next room, and a very bloated bass sound. I hated them. The D2000 is a far better headphone.
Mark Lawton did a great review of the D series, and found that mostly they are the same headphone, with different factory mods. I had my D2000 modded by his company which made the headphone way better, basically taking away the flaws it comes with from the factory (a bit loose bass, etc).
4. They do not need an amp, as they sound great straight from an iPod. However, like any can they do sound better with an amp.
Lastly, if you don't have the cash, buy the Audio-Technica M50 instead. It is by far the best headphone I've ever heard in it's price class, or even double it's price class. It is ALMOST as good as the D2000, which strong tight bass, great mids, nice highs. It also is far more comfortable, stays on when you lie down, and doesn't allow any sound leakage at all. It is a superbly designed headphone.
The ways the Denon's improve the M50 sound, is wider soundstage, a little less bloated bass, and slightly better highs. But that comes at the cost of leakage, comfort, and a more recessed midrange. So it's a toss up. The D2000 is overall a higher quality headphone, but the M50 is no slouch.
I don't have the K701 but I am in fact buying one tonight, to replace my MD2000 which I must now sell. I had an accident which hurt my ears, and I can no longer handle the Denon's powerful bass. The K701 is famous for very lean bass, and a wonderful sound, so I'm heading that direction sadly.
Hope that all helps out.