My Mac mail is sending replies with silly pictures in the top right hand corner. I can't delete them

That image (the picture) which you have associated with your account shows in your emails, but It is not transmitted in any emails that you send.

You can change the picture in System Preferences > Accounts. Select your account and choose another image.

But importantly whatever image is there, it is not transmitted in the email. It is shown to just pretty up your email for your viewing only.

At some point you have taken a self portrait from Photobooth. From memory I think that is when you set up your account.

As I said, you can choose another image to not be your photo.

As far as i know it cannot be removed from the email, but you can do either of two things. Choose another image that is not your photo.

1. (Choose another image)

Open System Preferences, click on Accounts, then your account name.

Click on the small photo on the right that will open up a panel of a variety of pictures and symbols, and choose one by clicking on it.

The photo has been replaced by your new selection. This new image will still appear on your emails but it won't be your photo.

2. (simulate a blank image)

The only way I know to not have a picture at all is too create an image which is white. The photo itself will likely reside in

~/Pictures/Photo Booth

or if not there have a look in

~/Library/Images/iChat Recent Pictures

I have seen it in both locations at different times depending on when it was produced.

It may be called Recent 1.tiff

Drag it to the Preview application to Open it

From the Edit menu choose

Select All

press Command X

press Command S

quit Preview.

Open System Preferences, click on Accounts, then your account name.

Click on the small photo on the right, to open the panel and where it says Edit Picture, click on that, and then drop down Recent Pictures, see your old photo in a set of squares, click on it and it will be updated to the white image. and choose Set.

No more image.

Roam, are you 100% certain it is the case that nobody else can see the image? I have suddenly started to see identically placed images of others from whom I receive Apple Mail.

If you receive an email from someone who is in your address book, and for whom there is an image there, you will see that image when you open their email. They have not sent the image, it's entirely local to you.