How important a player in the Middle East is Iran?
Iran is a very important player in the Middle East. This is so for three major reasons. First, it is a large and relatively prosperous country. Second, it is in a very strategic position, controlling the entry to the oil rich Persian Gulf. Finally, it is the major Shi'ite country in the region.
The first two of these make Iran an important power in the region regardless of any other considerations. Any country with a large military and a strategic location will always be important. The third factor makes Iran important far beyond its borders. Many countries in the region have large Shi'ite minorities (or a majority in the case of Iraq) that often look to Iran as a sponsor. There are Shi'ite terrorist groups, such as Hezbollah, that receive a great deal of support from Iran. Through such groups, Iran can project some amount of power as far as Lebanon.
In these ways, Iran is a very important power in the region.