I like Trello. I currently use a similar self-written system for ticketing and general task management based around scrum and kanban boards (scrumban). The main flaw I've had with it (and the reason for moving to something else) is the management of e-mail "conversations". Our calls often involve several e-mails pinging backwards and forwards between users, and the ability to have this managed inside a ticketing system will be a real benefit.
But the main flaw of ticketing systems is that they're not designed for scrum or kanban. Over 50% of our work is project based, so doesn't fit easily into a standard ticketing systems which is designed around quicker turnaround of calls. I love scrum for project management.
Between my system, Trello, Zendesk and Asana I can picture the perfect solution. However, there doesn't seem to be one single solution that ticks all my boxes. The only way I'll achieve this is by developing my own system, but the time to do that is really time I should be spending on other jobs.