iOS does not do this. Perhaps Apple considers it clutter. Apps come as standalone applications that do not even have much scope of working with each other, let alone modifying the system altogether. People on the Internet have been creating mockups of how widgets could work if they were added into iOS. Here's what I think.
Enter: Spotlight widgets!Some say widgets should be added to the Home screen. Some suggest Notification Center widgets, similar to the Stock and Weather widgets that come built into iPhone.
But why not utilize the neglected Spotlight area in iOS for add-ons? Swiping to the left beyond the first page of the Home screen brings up a mostly blank Spotlight area. It just has a search bar that lets the user search for apps, music, contacts and even Google and Wikipedia. The rest of the screen space is only used for search results.
Widgets will be of fixed width but developer-configurable height. User scrolls up and down through the widgets.
An advantage of this approach to a widget interface over Home screen widgets is that this does not look like ripping off Android.
How widgets could workI won't try to create mockups because I'm horrible at Photoshop.
When there are no search results, widgets could be displayed. Perhaps there could be a simple dictionary widget like the one that comes with OS X. iOS does have a built-in dictionary, which could be used for this.
There could be weather and stock widgets plus widgets that come with apps. Apple could choose to let developers bundle widgets within apps or they could create a new section of the App Store for widgets, like they did with Newsstand.
There can be a web-clip widget like the one in OS X. User can select a part of a website in Safari and add it as a widget. The widget always updates to reflect the website and tapping it opens the site in Safari.
The solution to accessibilityIt currently takes a number of taps/swipes to go to Spotlight: 1. Unlock phone (enter code if necessary), 2. Swipe right if currently on the first page of Home screen (otherwise get to first page then open Spotlight). The idea behind widgets is very quick access.
Apple could implement something similar to the camera icon on the Lock screen. Perhaps pulling down the bar that currently has the clock and music controls will take the user to Spotlight and widgets? This way, search and widgets will be a single gesture away, just like camera.
This solves another, smaller issue. Quick access to Spotlight may mean that the underused search function may get a lot more use. Based on what I have heard from many people on the Internet, Spotlight isn't used very frequently by most people. I don't have exact numbers for this, though and there might be a very high proportion of people who use it regularly.
What do you think of this proposed solution? Let me know in the comments.