As I was on HN in 2008 and paying attention to these sorts of things, I'll pretend I'm qualified to offer opinions.
1. A cure for the disease of which the RIAA is a symptom - Streaming, both paid and ad-supported seems to be the answer here. It's prone to monopolies and music streaming doesn't seem to pay artists very well, but Netflix is producing quite a bit of original content.
2. Simplified browsing - mobile ate this.
3. New news - appears largely unsolved. A few big national newspapers are are doing serious reporting, some newcomers (blogs) are doing the same without a print version and local newspapers are still mostly bad. Social sharing of news mostly hasn't made things better.
4. Outsourced IT - "the cloud" hasn't replaced everything, but increasingly, companies do seem to like software that stores data on someone else's server and gets delivered by a browser.
5. Enterprise software 2.0 - not a field I have enough contact with to comment on.
6. More variants of CRM - as above, I'm not very qualified to comment. I know there are startups doing things in this space.
7. Something your company needs that doesn't exist - kind of too vague to respond to. AirBnB was an example of this.
8. Dating - Tinder is the main winner I'm aware of. I'm not quite sure how they solved the chicken and egg issue, though it appears they were helped by Facebook-based login and doing their initial release to students at a small set of universities.
9. Photo/video sharing services. Instagram seems to be the biggest winner here. Imgur, started as image-hosting for reddit is trying to offer reddit-like features and keep the users on its own site.
10. Auctions - I think this one missed the mark a little. People don't want to auction things for the most part, they just want to sell things. As an online marketplace accessible to individuals, nothing has really displaced Ebay. Facebook is doing a bit for some niches with sale-oriented groups and built-in payments, and there's Etsy. It's possible to sell on Amazon as an individual, and a few people do, but Ebay still dominates.
11. Web Office apps - Google ate this, and Microsoft has entries in this space too.
12. Fix advertising - Facebook and other social platforms have at least made the problem different by having businesses interact with customers directly and paying for reach. This is not a solved problem by any means.
13. Online learning - massive open online courses are improving access to education, but the fact that a lot of situations still demand credentials from more traditional educational institutions is keeping this approach from being too dominant. I expect more development here long-term.
14. Tools for measurement - this seems like a feature more than a product. A lot of productivity tools have metrics built in, e.g. github.
15. Off the shelf security - there seem to be some things available here, but nothing really dominating the market.
16. A form of search that depends on design. I'm not certain, but I don't think there's anything here. What people seem to be more interested in is something that's not big, scary and delivering tailored results. That's not a huge market, and DuckDuckGo seems to have most of it.
17. New payment methods - Paypal is still big, Facebook handles payments now, mobile OS makers and device manufacturers are doing things. Stripe and Square helped with credit card processing, but that's not really a new payment method. Cryptocurrency is a thing, but nobody's been very successful actually using it as a payment method.
18. The WebOS - stuff like Zapier and ITTT are providing some plumbing, but nothing very OS-like.
19. Application and/or data hosting - "the cloud" is obviously huge and dominated by AWS and Google.
20. Shopping guides - I'm calling this a miss, with most of the exceptions being niches too small to be more than supplemental income for one person (http://flashlights.parametrek.com is a neat example, and the creator has an account on HN by the same name). Most people just shop on Amazon. There's low-quality content/affiliate marketing in this space, but that's arguably just SEO spam.
21. Finance software for individuals and small businesses - I'm not sure what's going on in this space. I haven't heard about anything making big waves.
22. A web-based Excel/database hybrid - Unless Google Sheets counts, I don't think this has panned out yet.
23. More open alternatives to Wikipedia - Deletionists still seem to rule Wikipedia, and nothing has displaced it.
24. A buffer against bad customer service - I'm not sure there's been much movement here. I suppose you could use something like Taskrabbit to hire someone to talk to Comcast for you.
25. A Craigslist competitor - Facebook groups have displaced Craigslist a bit and Ebay has experimented with some local marketplace stuff, but I think that's mostly it.
26. Better video chat - Google and Apple built better Skypes. There's appear.in, Discord offers video, etc.... There's a lot happening here, but it seems essentially evolutionary, not revolutionary.
27. Hardware/software hybrids - smartphones ate a lot of the applications for this, but Arduino and various single-board computers enabling DIY projects are cool.
28. Fixing email overload - I'm not seeing a single overarching solution here, but things like Gmail priority inbox, in-browser notifications and such seem to be chipping away at it.
29. Easy site builders for specific markets - I'm sure there are a few of these that are more niche. Shopify is kind of Viaweb 2.0. People in some niches seem to prefer to just have accounts on social media and have little interest in standalone websites.
30. Startups for startups - I probably haven't been paying attention to the right things to list these. A lot of stuff that's not very startup-specific like CRM, "cloud" services and finance software can, and probably does make inroads by being startup-friendly.