I'm relatively new to homebrewing and I tried a Muntons Extract Pilsner kit. I followed the instructions on the kit to a T and after 3 weeks (and having read other questions and comments on this site), my SG is still above 1.020. Can I salvage this batch still or should I just scrap it and start over?
Finishing around 1.020 isn't really a problem, many yeasts won't go much further than that, depending on the fermentability of the wort, available nutrients (and temperature and water quality and whether you played Bach or Beethoven to it...)
The real question is, how does it taste? If it's still sweet/bubbling/cloudy/foamy give it another week. If it's dry and not bubbling and not foamy and clear and the gravity has not changed for three days, bottle it. Enjoy.
But don't chuck it unless things go really badly - like horrible weird flavors or mushrooms growing on top.
What's your target FG? If you're off just a point or two, don't sweat it. If it's supposed to be 1.012 or something, try gently rocking your fermenter to bring your yeast back into solution. You might also try moving your fermenter someplace warmer if it's below 70F. You can also try taking a half-cup or so of table sugar, dissolving that in some warm water and adding it to your beer to try to jump-start your fermentation.
If you can't get it to drop any further, go ahead and bottle it, but keep your bottles in a plastic tub just in case you get any bottle bombs. I definitely wouldn't dump it, it's just a stuck fermentation, your beer is fine (just a little sweet).
Target FG is 1.008 and it's currently slightly over 1.020. It's sweet, still cloudy, not bubbling. Gravity hasn't changed since about a week ago. I don't know that bottling it now would allow for there being much of an ABV. Temp is down around 68 which should be fine for a pilsner lager/ale yeast (wouldn't it???) I might try to throw a bit more priming sugar in it and see if the fermentation will start up again. I did swirl the wort in the fermenter last week to try to bring the yeast back into solution but apparently it didn't work. Would you recommend maybe pitching another batch of yeast into the carboy to see if that will bring the SG down a bit more?