Autumn (Sept to Nov) and Spring (March to May) are the best seasons to do Everest Base Camp Trek. The weather is sunny and warm with outstanding views.
If you wish to avoid crowds and enjoy some alone time with nature then taking this trip during winter (Dec- Feb) could also be an another great option.
However, the temperature during winter could be harsh for most guests and there chance to get snow too. Trekking in the Summer or Monsoon seasons (June to Aug) will be affected by rain but the Summer trek could be a boon for a keen botanist.