Southeastern has a YouTube page including some recorded training videos and webinars. There are short videos on different aspects of using the SEAL system, as well as a full-length webinar. Upcoming webinars relevant to inter-library loan are announced over our CE and SEAL discussion lists.
OCLC has a variety of webinars available, including product updates on OCLC Worldshare and Tipasa. Recently OCLC has also been providing webinar versions of popular sessions at their Resource Sharing Conference. Upcoming webinars are announced at the above link and on the ILL-L list serv.
Atlas Systems periodically posts live, no cost webinars on best practices in ILLiad and upcoming Atlas product developments. Upcoming webinars can be viewed and signed up for at the link. Previous webinars can be viewed here.
NLM hosts many webinars, including ones related to DOCLINE, PubMed, and Resource Sharing more generally. You can view upcoming trainings on the NLM site, or by subscribing to DOCLINE email updates.
Webjunction has free courses and webinars available for all library staff. While there are no ILL classes currently, there are webinars and courses focused on soft skills that are useful in inter-library loan. These includes topics such as time management, customer service, and marketing. Previous webinars and trainings can be searched here.
RAILS has several webinars on their Youtube page that are relevant and useful to ILL practitioners. Some recent topics included copyright, privacy, and open access resources for ILL.