"Best" amp... There are SO many options now, at pretty much any price point, that you can even factor in personal preference.
For awhile, FiiO was super popular for great sound at a budget... and they've improved most of their lineup, the E11k (portable) and E09k (desktop) are good choices, I enjoyed my E12 with my AKG (see my review in my signature) until I decided to switch to desktop tube amps.
Then the Objective2 (O2) became the flavor of hype amp. I've never listened to it because the designer created it with no stated objective other than, basically, trashing other amp manufacturers and stating that he could design an amp sounding better and costing less. Even the "Objective" name was saying it was engineered by numbers versus "all" the other amps which were tuned subjectively by ear. By all accounts of people who owned an O2, the numbers didn't lie and offered a breakthrough price/performance ratio, described as an amp that didn't take away from the performance of headphones (with the exception of the most notoriously difficult to drive), but didn't add anything to the sound either. The fame of this amp blossomed even more as reviewers used it's transparent-to-the-native-performance nature as a reference baseline when making their reviews... Almost like as if you wanted to be a reviewer, you had to get used to FLAC files of Pink Floyd, ObjectiveDAC, Objective2 amp, and a Sennheiser HD600, and then base any product reviews off of changing one component of that audio chain and comparing to the control. Very scientific. Very clinical. But at the end of the day, the bigger picture of why we buy this stuff is to enjoy music/audio, and flat isn't going to be interesting for everyone. Besides the design compromises for sound quality (wiring layout is a mess... Is it a portable, or a desktop? Not ideal for either!), if you read user impressions you'll see a lot of people that love it, but after the honeymoon period ended there were also a fair number of people who found it too dry and bare, or boring and moved on. When I was on the AKG Q701 thread, the majority wanted a different amp because the Q701 highs were too bright and analytical, but some people stuck to their guns that the O2 was a good linear paring but eventually they'd want a different headphone. I got to borrow an ODAC once, but for some reason it wouldn't work with my computer (and probably was the fault of my computer, but that was the only DAC ever not to work), I'd like to hear an O2 someday but at this point I'm past needing it.
Throughout the past year, Schiit gear has been hailed as great value amps, the magni and modi in particular as similar-sounding but cheaper to the O2+ODAC combo. Mad Lust Envy raved about the M&M stack... I forget which few headphones he used with them, but he did use a few. They still stand as great values, though again on the revealing/analytical/possibly bright sounding side of sonic signatures. I have a fellow Pittsburgh Head-Fi'er who has the modi, and he got the Vali instead of the Magni. Now, the Vali I really liked! Maybe a little detail was sacrificed, and the "EEeeeeeeee..." sound of the first 30-45 seconds of warm-up and any physical impact to the amp is real, but the humble amp is musical and fun to listen to. I wouldn't call the Vali an end-game amp, and Schiit definitely designed it as a gateway to audiophile gear, but A/B-ing it against my more expensive tube amp still had 98% of what made the music more enjoyable for me and was clearly a better value, making me look like I had overspent on my tube amp (though at the end of the day, I still love mine). With an AKG, soundstage is a little less wide but also less oval and more circular, sweetens the highs a bit, and IMO is a good pairing.
Right now, I'm having a good time using my Creative E5 with my AKG K612, it does for me what the FiiO E17 did for Mad Lust Envy as an amp but also as a flexible everyday device. It's like they took the features of the FiiO E17, added a few more (Bluetooth, noise-canceling mic, optical in and out, USB connection for smartphones), used the FiiO E12 amp but made it slightly warmer, and added SBX surround for PC/Mac users. For gamers, it's a definitely capable quality device that also solves all the setup issues you might have, except it can't decode a surround signal from a console. Either stick with stereo, or the upcoming G5 which is supposed to be like an E5 + Dolby decoding... The G5 looks like a replacement/upgrade to the Astro Mixamp all-around with better sound quality and no extra amping needed, though I suspect an XBone setup is stick going to be a PITA.
I've also read good amp impressions about Garage1217 amps, Little Dot amps, Emotiva, Cayin, and more. For couch/living room setups, I prefer portable amps because they're easy to put away and re-attach, and I often check out HEAD-Fi user ClieOS for his portable amp reviews. For desktop setups like mine, where you've got your computer, console, monitor, and desk space all right there, the sky's the limit and I prefer to have some awesome powerful (but bigger-sized) stuff.
For awhile, FiiO was super popular for great sound at a budget... and they've improved most of their lineup, the E11k (portable) and E09k (desktop) are good choices, I enjoyed my E12 with my AKG (see my review in my signature) until I decided to switch to desktop tube amps.
Then the Objective2 (O2) became the flavor of hype amp. I've never listened to it because the designer created it with no stated objective other than, basically, trashing other amp manufacturers and stating that he could design an amp sounding better and costing less. Even the "Objective" name was saying it was engineered by numbers versus "all" the other amps which were tuned subjectively by ear. By all accounts of people who owned an O2, the numbers didn't lie and offered a breakthrough price/performance ratio, described as an amp that didn't take away from the performance of headphones (with the exception of the most notoriously difficult to drive), but didn't add anything to the sound either. The fame of this amp blossomed even more as reviewers used it's transparent-to-the-native-performance nature as a reference baseline when making their reviews... Almost like as if you wanted to be a reviewer, you had to get used to FLAC files of Pink Floyd, ObjectiveDAC, Objective2 amp, and a Sennheiser HD600, and then base any product reviews off of changing one component of that audio chain and comparing to the control. Very scientific. Very clinical. But at the end of the day, the bigger picture of why we buy this stuff is to enjoy music/audio, and flat isn't going to be interesting for everyone. Besides the design compromises for sound quality (wiring layout is a mess... Is it a portable, or a desktop? Not ideal for either!), if you read user impressions you'll see a lot of people that love it, but after the honeymoon period ended there were also a fair number of people who found it too dry and bare, or boring and moved on. When I was on the AKG Q701 thread, the majority wanted a different amp because the Q701 highs were too bright and analytical, but some people stuck to their guns that the O2 was a good linear paring but eventually they'd want a different headphone. I got to borrow an ODAC once, but for some reason it wouldn't work with my computer (and probably was the fault of my computer, but that was the only DAC ever not to work), I'd like to hear an O2 someday but at this point I'm past needing it.
Throughout the past year, Schiit gear has been hailed as great value amps, the magni and modi in particular as similar-sounding but cheaper to the O2+ODAC combo. Mad Lust Envy raved about the M&M stack... I forget which few headphones he used with them, but he did use a few. They still stand as great values, though again on the revealing/analytical/possibly bright sounding side of sonic signatures. I have a fellow Pittsburgh Head-Fi'er who has the modi, and he got the Vali instead of the Magni. Now, the Vali I really liked! Maybe a little detail was sacrificed, and the "EEeeeeeeee..." sound of the first 30-45 seconds of warm-up and any physical impact to the amp is real, but the humble amp is musical and fun to listen to. I wouldn't call the Vali an end-game amp, and Schiit definitely designed it as a gateway to audiophile gear, but A/B-ing it against my more expensive tube amp still had 98% of what made the music more enjoyable for me and was clearly a better value, making me look like I had overspent on my tube amp (though at the end of the day, I still love mine). With an AKG, soundstage is a little less wide but also less oval and more circular, sweetens the highs a bit, and IMO is a good pairing.
Right now, I'm having a good time using my Creative E5 with my AKG K612, it does for me what the FiiO E17 did for Mad Lust Envy as an amp but also as a flexible everyday device. It's like they took the features of the FiiO E17, added a few more (Bluetooth, noise-canceling mic, optical in and out, USB connection for smartphones), used the FiiO E12 amp but made it slightly warmer, and added SBX surround for PC/Mac users. For gamers, it's a definitely capable quality device that also solves all the setup issues you might have, except it can't decode a surround signal from a console. Either stick with stereo, or the upcoming G5 which is supposed to be like an E5 + Dolby decoding... The G5 looks like a replacement/upgrade to the Astro Mixamp all-around with better sound quality and no extra amping needed, though I suspect an XBone setup is stick going to be a PITA.
I've also read good amp impressions about Garage1217 amps, Little Dot amps, Emotiva, Cayin, and more. For couch/living room setups, I prefer portable amps because they're easy to put away and re-attach, and I often check out HEAD-Fi user ClieOS for his portable amp reviews. For desktop setups like mine, where you've got your computer, console, monitor, and desk space all right there, the sky's the limit and I prefer to have some awesome powerful (but bigger-sized) stuff.