Most of us out there tend to use lower budget headphones, most of the time the sound can be really quite good like the House of Marley ROAR headphones I reviewed recently but irrespective of how the headphones sound they are always going to be at the mercy of the device they're plugged into.
For the majority of us I think it will be a smartphone and the headphone amplifiers that are used aren't always the main focus of the manufacturers, it essentially boils down to a balancing act of hardware they squeeze into the ever thinner cases and powering all of that hardware using the little phone batteries they also squeeze into the middle of all that hardware goodness.
But if you want to get more punch and clarity out of your headphones there is the option to buy a headphone amp. These portable power units can prove to be a little inconvenient to carry around, but if you are willing to put up with that your headphones should perform much closer to their maximum potential.
If you like the 'sound' of this then the Fiio E6 is an excellent starting point. It is pretty compact (easily fits into the palm of your hand), lightweight, and is fitted with decent battery that will last quite a while.
The Fiio E6 is an entry-level amp so it's not going to have the most ground breaking sound enhancements, but it does offer some equalizer settings that can boost the treble and bass. Another EQ setting the Fiio E6 offers actually softens the volume, which can reduce the bass on bass-heavy headphones to make them sound well-rounded. It can also add plenty of gain, too. According to reviews from Head-Fi and TrustedReviews they have sung its praises over the years as a result.
So if your current set up just doesn't quite hit the mark then you mark the you might want to invest in a headphone amplifier, the Fiio E6 is available on Amazon for Between £20 to £30 which probably is less than you would have to pay to to upgrade to a better set of headphones.