When an aircraft is on the ground, with a headwind, that's airspeed that it already has. It doesn't need to be accelerated to the same degree to reach lift off speed, so a headwind will make the takeoff roll shorter. A tail wind has the opposite effect.
When landing, a headwind will reduce the ground speed, and means that the aircraft has less energy relative to the ground to get rid of, so less heat in brakes, shorter landing roll etc. A tailwind will add to the groundspeed, and means we'll need more runway. (There is normally a limit on acceptable tail winds placed by the manufacturers which is generally 15 knots).
A crosswind during take off will try to push you off the runway, so you'll sometimes need quite large control inputs to keep the aircraft straight. Those inputs will generate drag, and will reduce the takeoff performance, though not dramatically. You need to be careful rotating the aircraft as you will lose the control that having some wheels on the ground gives. Generally, though, not a big deal. Landing is a bit different. You can see aircraft appearing to 'crab' sideways towards a runway, but that's not exactly what they are doing. We turn into the wind, so that the resulting drift gives us a track down the runway. Every time there is a change in the wind, we have to turn to both fix the effect that the change had (it's moved us in one direction or the other before we can correct it), plus we have to then reestablish that correct track. At the crosswind limit, the drift will be around 15 degrees.
Just before touchdown we have to flare the aircraft. Once that's done, you need to use rudder to align the aircraft with the runway. That rudder input has to be done smoothly, as a secondary effect of any rudder input is roll, and you don't want any roll near the ground, and in particular, you don't want any towards the downwind side (and that's the effect that the straightening rudder will have). Of course, as soon as you even start to straighten the aircraft up, you're cancelling out your wind correction, and the wind will start to take you towards the downwind side of the runway. In smaller aircraft, that can corrected by a little bank in the opposite direction, but it's not really an option on the big quads because of engine ground clearance (pod scrapes). On the Boeings, you can actually land with all of the drift still intact, and whilst a bit uncomfortable at the back of the aircraft, it is a very viable technique. An Airbus driver might be able to confirm, but I think they are limited to 5 degress of drift at touchdown (???).
Even once down, the wind is still trying to push you to the side of the runway, so you may have to use quite large and abrupt control inputs to ensure the aircraft stays where you want it.
And all of this becomes much more interesting in the wet....
So, after all that, headwind is generally best. Light tailwinds are fine, but can become limiting very quickly, and crosswinds can be hard work.... but fun.