After a brief overview of the elements of modern grid computing, a number of common use-cases of natural language processing tasks running on the grid are presented, notably corpus annotation with morpho-syntactic tagging (600+ million-word corpus in one day), n-gram statistics processing of a corpus and web-accessible services with annotation and term-extraction as examples. Implementation considerations and common problems of using grid for this type of tasks are laid out. Finally, a simple action plan for evolving the infrastructure created for these experiments into a fully functional Human Language Technology grid Virtual Organization is given with the goal to make the power of European grid infrastructure available to the linguistic community.