Logistics and supply chain are the strongest reasons to keep European military bases. With our own bases, we can rapidly deploy wherever needed, and keep supplies flowing to troops engaged in military activities. It seems strange though that we have bases in Europe and elsewhere in the world, but as far as I know, we have no foreign bases in the US.

Local economic benefits are up to the host nation. If it wasn't in their best interest to have a base, then they wouldn't let us have one. Overall, bases strengthen our strategic position and give us an edge in global conflicts.

Speaking as a former US Marine, there are many reasons to retain a military presence in tactical locations around the world--including Europe. The foremost is that friendly countries change their minds all the time. In one scuffle country x is our buddy then in the next, country x is on the other side. Europe may have shown to be pro-US for the last 50 years, but that is a negligible amount of time historically.

It's mostly about logistical deployment. Say some ex-Soviet-Bloc country or region gets out of hand and attacks the US embassy there. The US would have to fly half way around the world to rescue civilians--including innocent tourists. With bases in Europe and beyond, the rescue teams can arrive in just a few hours--saving more American lives.

Additionally, the countries who harbor US military personnel gain economically from the business generated as well as can be assured strength should they be attacked or suffer some catastrophe.

The final reason for maintaining bases in Europe has nothing to do with any part of Europe. The military has several intelligence outposts in Europe which are focused on the Mideast, Asia, and Africa. These tools allow America to continue to collect information on terrorist organizations in conjunction with the EU for the safety of all.