I strongly encourage my friends and acquaintances to make blogs, and some of them have asked me for ideas. So here's a big list. Some I've already done, some I haven't. All can be tweaked to meet your needs. This list assumes yours is a general-purpose or personal blog - if you have a theme, only some will apply.
1. 100/50/25 Things About Me - people love lists, especially snappy, packed ones like this.
2. Current Affairs - write an opinion piece on something currently in the news. See, for example, my post about the marriage referendum.
3. Rant - you'll have loads to write on a subject you really care about. See my rant about Leaving Cert history.
4. Series - wonderful when you're short on posts. Pick a topic and write a group of related blog posts, e.g. "The World Cup", "Exams". See my "World Week" series.
5. Review - write down your thoughts about a piece of media. Some people (like me) get whole blogs out of writing reviews. It's not just books - you can review films, video games, albums ...
6. Photo - photo posts are great for when you're not in the mood to write much, and they're really great for the next type of post as they jog your memory. See my Photo Friday tag.
7. Memory - talk about a special memory. The blog post can act as a souvenir.
8. Interview - I love these. They're fun, and there's often little writing involved.
9. Explainer - find a topic, do your research, and share what you've learned, a la Wait But Why. Or explain something you understand really well to your readers.
10. Life - these make up a lot of my posts. Just talk about what happened to you that day. Great posts if something interesting happened.
11. Satire - these posts can be great fun. Just take the piss out of something. An example from my blog: How To Pull Weeds.
12. Tribute/Appreciation post - got something you really admire? Do a blog post explaining why! Here's one of mine: 12 Reasons Bo Burnham is Awesome.
13. Confessional - work your thoughts out on-screen. These can be risky, especially if you have a high public profile, but they offer plenty of benefits and are very cathartic. See: I Do Not Win Everything.
14. Journalistic - similar to #2, except this is a news report rather than an opinion piece. Go to an event in your vicinity and act as a journalist. Example: Head Girl Campaigns
15. Pros and Cons - these are great when you can't think of something to write about. Just pick any ambiguous topic and come up with pros and cons, like Pros and Cons of Long Summer Holidays.
16. Unique - if you've done anything unusual (started a company, won a big prize, gone to space, whatever) people would love to read about it. You can get loads of blog posts out of one of these experiences.
17. Quasi-sponsored - these are good for traffic. If you're a book reviewer, for example, Tweet the publisher with a link to your post. I got a lot of traffic when high-ups at BT Tweeted my posts about the Young Scientist. Anything relevant that you could attach a company name to, do.
18. Lists - lists are fabulous, both to read and to write. Cracked.com has made a thriving business out of it, as have plenty of other sites (like one I've written for, Listverse). Just look through my blog archives for list ideas.
19. Format Exploration - why not try writing a story or a poem once or twice? Or write your blog posts in the form of a table, like I did this week? It rejuvenates your creativity.
20. Brag - if you can't brag on your own blog, where can you? It's like your own little island on the internet.
21. Hobbies - this one is a no-brainer, really. Introduce the world to your hobbies! I've done that with chess and ukulele, and continuously do it with science and writing.
Those are all the categories of blog post that come to mind. Here are some specific ones I plan to write in the near future.
My Pet Peeves (Rant)
Tribute to My School (Tribute)
InspireFest HQ (Life)
Interview with Harry McCann about Digital Youth Council (Interview)
Sentinus N.I. (Life)
Beginnings of #repealthe8th (Opinion)
June Review etc. (Reviews)
Spotify: Likes and Dislikes (Opinion)
Trip to Seattle & Mentoring Day with Intellectual Ventures (Life)
Travel Bucket List
Jobs/Occupations (Interview + Series)
Discussion of Leaving Cert papers (possible interview)