Which biomedical ontologies should we use?

As a rule of thumb, for every single problem/term/use case, you will have 3-6 options to choose from, in some cases even more. The criteria for selecting a good ontology are very much dependent on your particular use case, but some concerns are generally relevant. A good first pass is to apply to "10 simple rules for selecting a Bio-ontology" by Malone et al, but I would further recommend to ask yourself the following:

• Do I need the ontology for grouping and semantic analysis? In this case a high quality hierarchy reflecting biological subsumption is imperative. We will explain later what this means, but in essence, you should be able to ask the following question: "All instances/occurrences of this concept in the ontology are also instances of all its parent classes. Everything that is true about the parent class is always also true about instances of the children." It is important for you to understand that, while OWL semantics imply the above, OWL is difficult and many ontologies "pretend" that the subclass link means something else (like a rule of thumb grouping relation).
• Can I handle multiple inheritance in my analysis? While I personally recommend to always consider multiple inheritance (i.e, allow a term to have more than one parent class), there are some analysis frameworks, in particular in the clinical domain, that make this hard. Some ontologies are inherently poly-hierarchical (such as Mondo), while others strive to be single inheritance (DO, ICD).
• Are key resources I am interested in using the ontology? Maybe the most important question that will drastically reduce the amount of data mapping work you will have to do: Does the resource you wish to integrate already annotate to a particular ontology? For example, EBI resources will be annotating phenotype data using EFO, which in turn used HPO identifiers. If your use case demands to integrate EBI databases, it is likely a good idea to consider using HPO as the reference ontology for your phenotype data.

Aside from aspects of your analysis, there is one more thing you should consider carefully: the open-ness of your ontology in question. As a user, you have quite a bit of power on the future trajectory of the domain, and therefore should seek to endorse and promote open standards as much as possible (for egotistic reasons as well: you don't want to have to suddenly pay for the ontologies that drive your semantic analyses). It is true that ontologies such as SNOMED have some great content, and, even more compellingly, some really great coverage. In fact, I would probably compare SNOMED not with any particular disease ontology, but with the OBO Foundry as a whole, and if you do that, it is a) cleaner, b) better integrated. But this comes at a cost. SNOMED is a commercial product - millions are being paid every year in license fees, and the more millions come, the better SNOMED will become - and the more drastic consequences will the lock-in have if one day you are forced to use SNOMED because OBO has fallen too far behind. Right now, the sum of all OBO ontologies is probably still richer and more valuable, given their use in many of the central biological databases (such as the ones hosted by the EBI) - but as SNOMED is seeping into the all aspects of genomics now (for example, it will soon be featured on OLS!) it will become increasingly important to actively promote the use of open biomedical ontologies - by contributing to them as well as by using them.