Attempts to negotiate in the conflicts about Israel - failed

Attempts to get more auxiliary troops from European countries - failed in several countries, little success in others

Attempt to get Georgia into NATO - failed

Attempts to keep "coalition of the willing" auxiliary forces in Iraq - quite failed, the number of non-U.S. coalition forces is shrinking

Attempts to mobilize Europe for an attack on Iran - failed, Europe prefers non-violent means

U.S. relevance in African conflicts (Sudan, Congo, Zimbabwe, Kenya)?
Marginal, except when it incited a conflict (the U.S.-backed invasion of Somalia by Ethiopia).

U.S. relevance in Latin America? - Probably close to the level of Venezuela...

U.S. relevance in Asian conflicts? Marginal, East Asian allies prefer their silent diplomacy with North Korea and PR China over U.S. diplomacy.

Situation in Europe? Almost all Bush-friendly governments lost to opposition (an exception was Major, who was still replaced).

Attempt to prevent North Korean nukes? - grand failure, the U.S. gave up and accepted that NK is likely now a nuclear power

Attempt to turn Pakistan against the Taleban? - miserable failure

Attempts to prevent several international treaties (like the Den Haag trials) - failure

Attempt to install a stable government in Iraq - still not successful

Attempt to install a stable government in Afghanistan - still not successful

Attempt to 'ally' with India - India was nice, but stays neutral.

It's naturally more difficult to tell about the failures because politicians don't talk much about denied demands in front of the press after the talks. But this list is still impressive in my opinion. It focuses on the security policy area, an area that received a lot of attention by the U.S. government in the past years. Still, lots of failures to exert influence.

The relevant successes happened in the 2002-2004 time frame (bases and overflight rights in Central Asia, Lybia scrapping a questionable nuclear arms program, support for GWOT, limited support for Iraq invasion).