What to do with failed/unwanted 3D prints?
The "obvious" answer is re-grinding the prints and making more filament. Unfortunately, this isn't yet a very economical or simple operation. A decent filament extruder capable of holding acceptable diameter tolerances is around $1000, and even then they can be pretty fidgety to operate. You have to have a LOT of volume throughput in your filament extruder for regrinding to be an economical proposition. 

Some of the reasons why recycling prints into filament can be difficult:


Most plastics will degrade to some extent each time they are extruded. (Both by the 3d printer and by the filament extruder.) PLA will thermally degrade with extended exposure to heat. PET will hydrolyze and break down if not meticulously dried to remove moisture prior to heating to the melting temp. (PETG seems to be less prone to hydrolysis damage than plastic bottle PET, but it still happens to a limited degree.) ABS holds up to extrusion conditions better than most, which is part of why it's favored for injection molding, but there's still the potential to affect properties by depleting additives or cooking out plasticizers. In practice, this means regrinds generally need to be mixed with fresh pellets at some ratio. That dilutes the degraded or additive-depleted polymer with good material so you can maintain the material properties and performance. 
If you print a variety of different colors, and don't want all your recycled filament to mix and end up a muddy brownish color, it can be difficult to manage the color sorting and matching. Most people don't want different colors along the length of a spool, either. So the regrind has to be mixed evenly in with virgin pellets and a suitable amount of masterbatch colorant to get a reasonable color output. You're not going to run off a new spool with 95% virgin pellets just to recycle a 50 gram failed print, are you? Likewise for material matching. Mixing materials is a bad idea. If you only print white PLA, this is all pretty easy to manage. But if you print a variety of colors and materials, you've got to set up a material tracking, sorting, and storage operation. You can do it... it's just a hassle. 
Diameter control is difficult. 3D printers need a fairly tight diameter control for reliable performance and good quality. This is really the key challenge in any filament extrusion process. Extruded polymers like to change shape as they extrude and cool due to molecular alignment effects. You can't just push molten plastic out a 1.75mm nozzle -- "die swell" will make the extrudate bulge to a larger diameter immediately upon exiting the nozzle. Then you have to actually pull on the soft filament as it cools to carefully draw it down to the right diameter. The way the filament extruder measures diameter and controls tension is the key to getting acceptable results. Most hobbyist/desktop filament extruders have not succeeded at this. 


Those are just the major issues. Filament extrusion is a complex subject with a lot of depth. For a home user of 3d printers, making filament basically becomes a whole second hobby. In my opinion, it only really makes sense in a commercial production printing environment where paid technicians can run the extruder(s) and a very large print throughput makes the pellets+regrind economics much more favorable than just buying new filament. 

Reducing and reusing are preferable to recycling. Making your printer more reliable and gaining experience with calibration/configuration will reduce the volume of waste produced. 

There are also some productive uses that let you reuse unwanted prints as-is or "downcycle" them for productive uses. 


I personally keep a box of failed prints (and calibration prints and
no-longer-needed prototypes) as showpieces for people who want to
learn about 3D printing, and as toys for my nieces and nephews. I strongly recommend doing your calibration prints with a "toy" calibration model like Benchy or CaliBlocks. 3D printing is still new enough that people will happily take dozens of Benchies off your hands for the novelty value.
Failed and unwanted prints can also be used around the workshop for shims, sacrificial
cushions when clamping or hammering or drilling, or as scrap for experimenting
with adhesives or post-processing techniques.
ABS scraps are good for making ABS-slurry as a print bed adhesion treatment
layer, or for solvent-painting and filling gaps in other prints. Unfortunately, most other filaments do not have such convenient and safe solvents.
Some people have experimented with putting piles of scrap prints on a cookie sheet in an oven and melting them into multicolor cutting boards. There's a lot you can do with this sort of heavy remelt plate if you get creative. (I personally wouldn't use cheap Asian filaments for food contact though, they often have unpleasant contaminants.)