Update: Blogger has introduced an easier way to delete labels. Sign into Dashboard, go to POST > EDIT POST which will cause all the posts to be displayed. At the top, next to the LABEL ACTION drop-down box (see screenshot below), click SELECT ALL, click the drop-down arrow, scroll to the lower half where you can see REMOVE LABELS with the list of labels below it. Click on the label you wish to remove and the selected label will be deleted from all posts:
To remove a label is simple. All you have to do is to edit all the posts that contain the label you want to remove, remove the label from the "Labels for this post:" at the bottom of the post and publish. When you are done, the label will be removed from your Label List.
To edit more than 1 post at the same time, refer to Remove labels the easy way via Label Action in Dashboard
Note: The easiest way to edit all the post with a particular label is to, first sign into blogger.com (Dashboard), go the the blog where you want ot remove the label, click on the label in the Label List, which will then display all the posts with that label in the same page, Click the quick edit pencil icon and you will get into the post editor window of that post. At the bottom of the post editor will be a box with all the labels tied to that post. just delete the label you no longer want. Repeat this with all the other posts that have the label you want to remove and when you have finished, the label should be gone.
If you don't see a quick edit pencil icon at the bottom of the posts, you have not enabled quick editing for that blog (this should already be enabled by default if you have not changed this setting, but it is hard to say). Click the SETTINGS tab, and by default, you will straight away be in the BASIC sub-tab. Look for "Add your Blog to our listings?" which should be the third settings, click the down arrow in the menu bar (box) to the left and select YES. At the bottom, click SAVE SETTINGS.
How to remove label countsFrom a commentator:
Sign into Dashboard, click LAYOUT then EDIT HTML to open the template editor. Look for the line of code (use ctrl+F to quickly find):
Delete that line of code to remove label count (see screen shot below):