"No amp necessary" requires a complicated answer!
For example, I have Sennheiser HD 580 ($150 used), and a Sennheiser SX 100 ($50 new).
When the 580 is driven without amp by the Sansa Clip 4gb, it sounds great, but the volume at 100% is just about right when I am in a mellow mood, but not loud enough if I am in a more assertive mood. However, if I am willing to live with the "medium" volume of the clip with the HD 580s, they sound MUCH, MUCH better than the Clip with the SX 100s.... which play much louder than the 580s do.
So it is a tradeoff of volume vs. quality. There is no diminution of bass in the 580s without amp (at least not with the Sansa Clip) ... it is just that at lower total volume, the bass is not as impactful as it is at higher volumes. Can you live with medium volume? Then go for HD 580s used and you'll have all you ever want. When I play the HD 580s out of the clip but through a good amp in between (such as the Portaphile Maxed Out) I can get about 50% more volume, but when I adjust the volume to match the Clip (about 60%), the QUALITY of the sound is the same.
Need the extra midbass thump from higher volume? Then I guess HD555 would be fine.... but not nearly the nuance, detail, or sense of spaciousness provided by the HD 580s.