Count based word embeddings depends on the frequency of the word in the sentence / paragraph / documents. There are several methods for count based word embeddings:

1. Bag of Words
2. TF-IDF

Limitations:

1. Lack of context and word order
2. Lack of semantic understanding
3. Doesn't account for Homonym or Polysemy
4. Limitation of Vocabulary
5. Poor performance with short text

References