TXT records are defined in RFC 1464.  Original usages were host descriptions, hardware types, and notes.  I'm glad people are still being creative with TXT records.  Here's a few popular usages:

Routing

The Route Views Project offers the lookup of IP addresses to autonomous system numbers and prefixes via DNS TXT records:

(destiny:22:17)% host -t txt 182.189.9.69.asn.routeviews.org.
182.189.9.69.asn.routeviews.org descriptive text "29791" "69.9.160.0" "19"
(destiny:22:17)% host -t txt 182.189.9.69.aspath.routeviews.org. 
182.189.9.69.aspath.routeviews.org descriptive text "13237 29791" "69.9.160.0" "19"

The above means 69.9.189.182 is advertised as part of 69.9.160/19, originated from AS29791, and might be reached through AS13237, from the perspective of one of the route views nodes.

Wikipedia

Yes, you can get Wikipedia articles via TXT records:

(destiny:22:24)% host -t txt Internet.wp.dg.cx.
Internet.wp.dg.cx descriptive text "The Internet is a global system of interconnected computer networks that interchange data by packet switching using the standardized Internet Protocol Suite (TCP/IP). It is a \"network of networks\" that consists of millions of private and public, academic," " business, and government networks of local to global scope that are linked by copper wires, fiber-optic cables, wireless... http://a.vu/w:Internet"

DNSBLs

Most people know about this one.  A DNS Blacklist is a way of easily looking up an IP address to see if it's been blacklisted by a particular list.  Great for mail servers to mitigate spam.

SPF

The Sender Policy Framework uses TXT records that are published to help prevent address forgery.

Update 2019-05-14

I've been informed that OpenSPF.org is gone now and to include the following link in this article:

What SPF Resources Are Available Now That OpenSPF.org Is Gone?

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