iOS: We're fans of the Brightnest web app for keeping track of what needs to get done around the house. Now, the service has an iPhone app that works seamlessly alongside it.
The app works in tandem with the free web app, so you'll need an account on Brightnest to use it. Once you're set up, you fill out a short questionnaire asking about your house (or rental apartment) so Brightnest can suggest tasks that you need to do. These range from reminding you to check your smoke detectors to cleaning up your refrigerators coils. From there, you can set reminders for regular maintenance throughout the year.
You can customise the app to feed you information you care about too, so if you're not a fan of the crafty stuff, for example, you can choose content that concentrates on making your house a more energy efficient. It's packed with clever uses for cleaning too, so you can even just use it as a repository of cleaning tricks.
The app will ask you for a US zip code during the setup, but most of the content is useful for everyone, no matter where you are in the world. I just used "90210", the only US zip code I could remember off the top of my head.
Home Maintenance by BrightNest - Home organisation, Cleaning Schedule, DIY Crafts and Home Design (free) [iTunes App Store]