It's been a requested feature for years[1] and now it's available thanks to some funds from Wikimedia Italia on Twitter: http://twitter.com/itwikiquote There are currently other four languages: http://twitter.com/WikimediaItalia/wikiquote
Twitter is a very obnoxious platform and probably not the best possible choice, but at least it has a RSS feed (when it doesn't time out) and I've created some feeds on FF (http://friendfeed.com/wikiquoteqotd/subscribers ) and identi.ca (http://identi.ca/group/wqd ). As you can see, we currently have some problems with long quotations and we're not including links to the Wikiquote page (which is obviously necessary to give the source, something we really care about); both should be fixed in few days. Moreover, for some reason Twitterfeed is currently not able to send some feeds to identi.ca, where now only @itwikiquote works (this is being worked out as well), and there are some additional problems with parsing some formats (e.g. the fr.quote templates).
When the service is acceptable, I suggest to link it from your main page, beside the quote of the day. It's a good service for users and it can bring some good traffic to your pages (provided that you have pages about the authors you quote, obviously). If you have concerns with advertising a proprietary platform like Twitter or FriendFeed, you can just link the RSS/Atom feed on identi.ca.
Nemo
[1] If I remember correctly, there used to be some French service which disappared some years ago.