The daddy-longlegs has the world's most powerful venom, but fortunately its jaws (fangs) are so small that it can't bite you.
This tale has been lurking around for years. I have heard it repeatedly in the United States and even heard a schoolteacher misinforming her class at a museum in Brisbane, Australia. This is incorrect, but to clarify it, several points need to be explained first.
Fact: That is a full-fledged Urban
Legend, with no basis in fact whatever. This legend is so widespread
that many people believe it who should really know better, including
some teachers and TV documentary producers.
Three different unrelated groups are called
"daddy-longlegs." Harvestmen (first picture) have no venom of any kind.
None at all! Same with crane flies (last picture). Pholcid spiders
(second picture) have venom (like almost all spiders) but there's
nothing special about it; in fact, a recent study showed that pholcid
venom is unusually weak in its effect on insects. This myth is debunked
at greater length on
Rick Vetter's web site.