As Doug M. pointed out, influenza would have to be high on the list of any possible pandemics. Anything else which goes airborne would be another good candidate, particularly if it has a decent incubation period to allow it to spread further.
Another possibility is a virus which makes the jump from animals to humans in a form which leads to a pandemic. There are a host of animal-borne viruses around which are capable of infecting and killing humans. In their current state, most such viruses are not capable of using human-to-human transmission, but it's always a possibility that a particular virus can make that jump. That is, after all, how most human epidemic viral diseases got their start.
Bat-borne virus are, for some reason, particularly capable of becoming infectious to other mammal species (including humans). SARS is a recent epidemic which almost became a pandemic, but was fortunately contained in time. The SARS virus originated in bats, and was spread to humans either directly or via civets. Ebola, one of the nastiest pieces of work around, is also spread via bats, as are a number of other viruses.
Perhaps the nastiest candidate for a bat-borne virus which evolves into a human pandemic is Nipah virus. This is a particularly ugly virus in its effects, which first came to major attention in 1999, when it caused an outbreak of encephalitis and respiratory disease in Malaysia, killing over 100 people and leading to the culling of millions of pigs.
Nipah virus has a natural reservoir in fruit bats (flying foxes), and its is easily capable of making the jump to humans. Since 1999, there have been eight further significant outbreaks causing multiple human fatalities, concentrated in Bangladesh and India, and a variety of other isolated cases. The virus has rather a high mortality rate; up to 90% in some outbreaks, although varying strains seem to have different mortality rates. In at least one of these epidemics, the virus is known to have turned into a airborne form transmitted from person to person.
Nipah virus symptoms are mostly respiratory and nervous system infections. It causes fever, headaches, severe coughing, blurred vision, and can send people comatose where they need mechanical ventilation to survive (if even that works).
It can also cause long-term encephalitis (nervous system infection); one person suffered from relapse encephalitis over 4 years after the original infection. There is no cure whatsoever for the relapse encephalitis, only treatment of symptoms [1]. It is not yet clear whether the virus in its encephalitic form is capable of reinfecting other people (hopefully not; if it does, then quarantine will become virtually impossible in the event of a pandemic).
Given that Nipah virus is already capable of evolving into a form where it jumps from person to person, all that it really needs to turn into a pandemic would really be a form where it is slightly less lethal. Its mortality rate is high enough that it probably kills people too quickly to spread far. But given that there are a variety of strains with varying mortality rate, all it takes is one that evolves a slightly longer incubation period, and you have the makings of a very nasty pandemic indeed.
This idea is one which I've toyed with writing a WI thread about, because the effects would be... bad. (But also rather morbid, which is why I've never turned it into a full thread.) It would be perfectly possible for Nipah virus to evolve into a pandemic which kills more than 20% of the global population, if it's not caught in time.
[1] This probably sounds familiar to anyone who's read Lands of Red and Gold. With good reason; that TL's Marnitja virus is based on an ATL version of Hendra virus and Nipah virus, one that emerged long enough ago in an urbanised society so that it could mutate into a major killer.