I switched to Pinboard (http://pinboard.in) in April and I highly recommend it. It's not free, but it's well worth looking at. (The pricing is a one-time fee that climbs as the site grows. It's currently $6.89. There's also a service to archive your bookmarks, but I haven't tried that. That's $25 a year currently.)
Here's their (probably about to be updated) "Should you switch from Delicious?" page: http://pinboard.in/switch/
This has to be great news for Pinboard - I'm not sure how much they raise the price with each purchase, but less than 30 minutes later and the current price is already $6.92.
So far it's holding up (about 40 hps) but we seem to be getting these intermittent connection drops. Waiting for things to calm down a bit before we start monkeying with configuration.
In order to arrive at economies of scale, you have to first provide for the expenses of ramp-up. So far, admission is nominal for the value its payers perceive. Plotting growth against current cost should give a pretty good forecast of how much is too much. Of course, under the current special circumstances, we could even see a freeze.
Pinboard is a service I've been wanting to purchase for years, but I never have because of how I've seen pvg (one of the founders) act on HN. The anti-hive mind attitude is desperately needed, but it's not a blanket license to disagree with everything without so much as a critical thought. I'm still trying to decide whether this is petty of me because it seems to be a really well done service.
Since the "it's not free but..." angle has already been played I'll add to kqr2's question...
Where are the best free places to migrate all of your Delicious bookmarks?
------EDIT---
OK, at a minimum you can go here: https://secure.delicious.com/settings/bookmarks/export and download your entire collection (importantly... with tags). This will at least preserve your content and, since I think many of us on HN are of the technical sort, permit you to scrape the data at your leisure. You get a massive (well, in my case) definition list of elements with the following included as attributes on the item's anchor tag: the url, the add date (ADD_DATE=) the private status of the link (PRIVATE=) and the tags (TAGS=). You also get a text description. Very nice!
http://historio.us/ is free (if you have fewer than 300 bookmarks). I don't think you'll find a totally free solution, as that's basically why delicious is closing :(
I'm VERY happy with Xmarks - esp. the cross-browser synching (i.e. all bookmarks are both local and in the cloud, and available in any browser).
I was also happy to pay for the service following the LastPass acquisition.
It works for me because I don't tag. Instead, I have a stable set of folders into which bookmarks get sorted. At this point, if something doesn't fit one of these categories, it's probably not relevant to me.
If you're looking for a somewhat different paradigm, try http://historio.us/. It's a search engine for bookmarks, so you can search in the entire content of the page instead of browse the titles.
They discontinued the delicious import tool for some reason -- some technical reason from what I understand.
However, if you apply for an API key, there are scripts out there that can parse the delicious export and import into Evernote, including tags. Google for 'delicious export evernote script'.