What possible features can be extracted from nucleotide sequences for machine learning?
For example gc content, dinucleotide frequency etc.
There are multiple ways to compile your features: 

1) ***Knowledge-based approach***: here you would only use a set of limited features that have a direct influence on your prediction/classification/learning task. Feature set will be limited, and you won't be able to add new knowledge to the field. 
[See][1] an example where we used a subset of features that we assumed to have role in 3D domain swapping 

2) ***Data-driven approach***: you can compile all available features that you can gather from your nucleotides (DNA or RNA?) and test them using rigorous feature selection method 
[See][2] an example where we used the entire set of features with hybrid features (combining multiple features) to predict 3D domain swapping 

3) ***Feature engineering/representation learning***: you can either of the above set and use [deep neural encoding][3] methods, here the algorithm would engineer the features ([NN, RBM, PCA, LSTM, etc.][4]). This approach is more applicable when you have large dataset(s) and not primarily looking for features contributing to your predictive model  such as feature selection or biological inference.   

- Count(s) of individual bases (ATGC - mono, bi, tri...) 
- k-mer count (See previous answers) 
- [physicochemical properties][5] of your sequences 
- evolutionary scores (example [here][6])
- mutation/substitution scores (GERP, PhyloP, etc.) 
- [Annotation][7]-based features (part of gene-structure (exon-intron), coding or [non-coding][8] etc.) 

PS. Like one of the answers, it all depends on your prediction problem


  [1]: http://www.ncbi.nlm.nih.gov/pubmed/20634983
  [2]: http://www.ncbi.nlm.nih.gov/pubmed/21592079
  [3]: https://t.co/YTs2xDLcai
  [4]: https://en.wikipedia.org/wiki/Feature_learning
  [5]: http://www.annualreviews.org/doi/abs/10.1146/annurev.bi.36.070167.002203
  [6]: http://www.ncbi.nlm.nih.gov/pmc/articles/PMC3145250/
  [7]: http://www.ncbi.nlm.nih.gov/pubmed/26494363
  [8]: http://www.nature.com/nmeth/journal/v11/n3/full/nmeth.2832.html