Contrary to popular belief, "daddy longlegs" (technically called harvestmen) aren't spiders. They live in the same kingdom (Animal), phylum (Arthropoda) and class (Arachnida) as spiders, but they branch out at order (Araneae for spiders; Opiliones for daddy longlegs).
They certainly LOOK like spiders – one tends to get kicked out of the Arachnid party if one doesn't possess 8 legs – but don't be fooled. While I'll kill any spider that crosses my path, if I happen across a daddy longlegs I'll let it be (if it's outside) or gently capture and release (if it's in the house). So there you go. Solid proof daddy longlegs are NOT spiders. Of course, there are a lot of other technical reasons they differ from spiders (like they don't spin silk and aren't venomous)...but let's not get carried away.
This random post and clarification research – that is, research performed to ensure I actually knew what I was talking about, to double-check the whole phylum-class-order thing and some other stuff – brought to you by Answers.com and Wikipedia (read more about harvestmen).