iOS 6 now allows attaching an email from within the Mail app. Tap and hold for the pop-up menu, just like you do for paste, then choose the arrow to the right for more options.
You can also tap and hold on a picture in the Photos app, then choose copy. Choose paste in the Mail app to copy the picture into the body of the email. This works in iOS 5.
For other files, or pre-iOS 6, the method that I think works best it to upload the file to DropBox, then use the DropBox app to get and and paste the share link into your email. This results in faster email delivery, and lets the other person download the file at their connivence, when they have a good internet connection.