motionBegan: Not Working

I assume you want to implement this in a subclass of UIViewController. Make the UIViewController capable of becoming first responder:

- (BOOL)canBecomeFirstResponder {
     return YES;
}

Make the UIViewController become first responder in viewDidAppear:.

- (void)viewDidAppear:(BOOL)animated {
    [super viewDidAppear:animated];
    [self becomeFirstResponder];
}

If the view contains any element, such as a UITextField, that might become first responder itself, ensure that element resigns first responder at some point. With a UITextField, for example, the UIViewController would need to implement the UITextFieldDelegate protocol, and actually be the delegate. Then, in textFieldShouldReturn:

- (BOOL)textFieldShouldReturn:(UITextField *)theTextField {
    // Hides the keyboard
    [theTextField resignFirstResponder];
    // Returns first responder status to self so that shake events register here
    [self becomeFirstResponder];
    return YES;
}

Implement motionEnded:withEvent:

- (void)motionEnded:(UIEventSubtype)motion withEvent:(UIEvent *)event {
    if ( event.subtype == UIEventSubtypeMotionShake ) {
    // Do something
    }

    if ([super respondsToSelector:@selector(motionEnded:withEvent:)]) {
        [super motionEnded:motion withEvent:event];
    }
}

There is a good post by Matt Drance of Apple in the iPhone Developer Forums (requires registration as a developer).

Update: implementing in a subclass of UIView

As discussed in the comments, this also works, not too surprisingly, in a subclass of UIView. Here’s how to construct a minimal example.

Create a new View-based Application project, call it ShakeTest. Create a new subclass of UIView, call it ShakeView. Make ShakeView.h look like this:

#import <UIKit/UIKit.h>
@interface ShakeView : UIView {
}
@end

Make ShakeView.m look like this:

#import "ShakeView.h"
@implementation ShakeView
- (BOOL)canBecomeFirstResponder {
    return YES;
}
- (void)motionEnded:(UIEventSubtype)motion withEvent:(UIEvent *)event {
    if ( event.subtype == UIEventSubtypeMotionShake ) {
        NSLog(@"Shake!");
    }

    if ([super respondsToSelector:@selector(motionEnded:withEvent:)]) {
        [super motionEnded:motion withEvent:event];
    }
}
@end

Make ShakeTestViewController.h look like this:

#import <UIKit/UIKit.h>
#include "ShakeView.h"
@interface ShakeTestViewController : UIViewController {
    ShakeView *s;
}
@end

Make ShakeTestViewController.m look like this:

#import "ShakeTestViewController.h"
@implementation ShakeTestViewController
- (void)viewDidLoad {
    [super viewDidLoad];
    s = [[ShakeView alloc] init];
    [[self view] addSubview:s];
    [s becomeFirstResponder];
}
- (void)dealloc {
    [s release];
    [super dealloc];
}
@end

Build and run. Hit Cmd-Ctrl-Z to shake the iPhone simulator. Marvel at the log message.