For ultimate spread and mortality, you want something that has the following properties in combination:
- High probability of infection when somebody is exposed to the disease (highly infectious)
- High probability of transmission of the disease after being exposed, but before developing visible symptoms (highly infectious during the incubation period)
- Long period between initial exposure and the disease manifesting itself (long incubation period)
- Difficult (medically, politically or otherwise) to quarantine and cure infected (and potentially infected) individuals once the disease manifests itself (hat tip to Jay for this one)
- High probability of death after the disease manifests itself (high mortality)
Also, a quick course of the disease once symptoms start to develop might make such a disease harder to prevent, because it provides less window of opportunity for treatment even if the disease is nominally treatable. It will also help if the early symptoms are similar to those of less dangerous diseases.
Ebola makes a poor epidemic fatal disease because while mortality is high, it quickly becomes clear that you are suffering from it, allowing for quarantine protocols to be initiated relatively early.
The common flu makes a poor epidemic fatal disease not least because with the exception of those who are for some reason already infirm, it isn't particularly deadly.
Thankfully to support what you want, presently, long-distance travel is the norm. A human who is infected by a disease in one part of the world can begin spreading it in a completely different part of the world within 12-24 hours under the right circumstances, making it difficult to establish proper quarantine of infected individuals. Under "ideal" circumstances, even the travel itself can easily transfer the disease to hundreds of individuals (a full airplane's worth). As Monica Cellio pointed out in a comment, an early outbreak at a place and time with a large worldwide attendance -- such as for example a major sports or religious event -- could exacerbate this.
The hard part is for the disease to be sufficiently deadly, yet not kill or incapacitate its hosts before the hosts have had time to sufficiently expose other potential hosts to the disease. If the disease fails the second criterion, outbreaks will be short and relatively geographically isolated. (There may be several related outbreaks in various parts of the world based on travel, but the disease is unlikely to significantly spread further before the outbreak dwindles down.)