What have you tried already?
First, does an alternative work:
Open your spreadsheet in Calc
Highlight the two (or more) adjacent cells
Click the Format pull-down menu
Click "Merge Cells"
Second (not to insult your intelligence), are you sure you are looking at the merge cells icon.

Third, do you have any special formatting in any of the cells you are trying to merge?
If someone posts a fix for your question, then please post a quick thank you and then go to your first post, use the edit button to add [Solved] as the first word of the title so other people can rely on the fix as well.
LibreOffice 3.3.3 on Fedora