For MongoDB, there isn't a full full-text indexing feature yet, however there's possibly one in the pipeline, perhaps due in v2.2.
In the meantime, you can create a simple inverted index by using a string array field, and putting an index on it, as described here: Full Text Search in Mongo
Or, you could maintain a parallel full-text index in a dedicated Solr or Lucene index, and if you're feeling really ambitious replicate directly to your full-text store from the Mongo oplog. Otherwise, populate both and keep in sync from your application logic.