If you amp, you'll definitely want a DAC to run your computer audio. Most computer sound cards are very poor at their headphone amplification and even line out. Plus, they can pick up all the internal noise from your computer, which you can definitely hear through headphones.
But, as to your question, I think all headphones do benefit from amping. Some benefit greatly, whereas some only slightly benefit. I do think amping is almost always an improvement.
I know there are some very high quality OPAMPS out there, but I have not had the fortune to hear them. Unfortunately, every OPAMP I have heard is very noticeable. The sound is usually a little flat, compressed, and lacks air. I really enjoy the sound from OPAMP-less class A and class AB amps, even when driving headphones that sound decent on an OPAMP. They just sound better with proper amping.
Sorry to ramble...I'm just a believer in proper amping. Based on the gear I've owned and used, I've not met an OPAMP or computer sound card that I've liked. I'm sure great ones exist, however.