Bremen is not the busiest airport in Germany, so there isnt much to write about, really. Since it is not quite so hectic, the Lufthansa staff here seem to have more time to be friendly. Its a very neat and tidy airport and has all the usual shopping and eating facilities. My information is just a little dated. The airport was being expanded when I was there last. One enduring memory I have of Bremen airport was when the pilot smacked the plane down on the runway while landing and the LH stewardess announced a hard, but hearty welcome to Bremen.
Unlike some German airports, it does not have a subway to downtown. A taxi costs 15-20 Euros. There is a good tram connection that probably costs 2-3 Euros, and it is possible to take luggage onto it. Buy your ticket at the automatic ticket machine. Also remember to cancel your ticket in one of the little gadgets called Entwerten. Theres an arrow on the ticket that shows you how to insert the ticket. The gadget stamps the date and time on the ticket.
This airport is a good alternative to Hamburg if you want to travel more towards the west, i.e. towards Holland.