Stripe is an awesome example of a company that addressed a tangible frustration / real need instead of a desire or a higher-level "want". I've noticed that companies that provide "Internet plumbing" often fall into this category:
* SendGrid (bulk email sending)
* Twilio (easy to use telephony / sms)
* Zencoder (video encoding)
* MailChimp (mailing list management)
What others can you think of? Would love to see a list here :).