With a little imagination, teachers can create fun lessons that integrate conversation skills with global issues content, no matter what level the class is. Through trial, error, and determination, I have found that many basic conversation games and activities used by EFL teachers can be adapted to fit global issue content courses. Basically, it is a matter of slipping global content into activities commonly used in conversation classes.
I teach an environmental studies class which concentrates on using environmental content and issues as a springboard for improving communication skills. I recently wanted my students to understand and communicate about endangered species and found the "Find Someone Who..." activity very useful. After pre-teaching necessary vocabulary, I gave each student a card like the following with a picture of the endangered animal they represented:

You are an African elephant.
You are endangered because of habitat destruction and poaching for your ivory.

You are an Atlantic bluefin tuna.
You are endangered because of overfishing.

Students received the following handout and then had to walk round the class talking to classmates and writing down the name of each endangered species they found.
Find Someone Who is...

Another good speaking activity is the guessing game "20 Questions". My environmental studies students play this to practice vocabulary related to animal classification. One student assumes the role of an animal while the other students ask Yes-No questions to guess what animal it is:

Jig saw activities offer another opportunity for mixing content with conversation skills. For my environmental studies class, I cut two sets of pictures out of a nature magazine. One set was about scientists trying to restore bald eagles to US states where they no longer live. The other was about marine biologists trying to preserve habitat for sea horses. Using these pictures, I made a poster for each story and placed these at opposite ends of the class. Alongside each poster, I placed a cassette player and a tape recording, explaining the pictures, which I had prepared earlier using vocabulary I felt most students would know.
After preteaching new vocabulary, I divided the class into two groups, the eagle and sea horse groups, but assigned each student a partner from the other group. Then, I explained that half the class would listen to one tape while taking notes so that they could explain their pictures and stories in pairs to the other half. Each group was allowed to play the tape as often as they wished. Once they were ready, I paired up each eagle student with a sea horse student and had them explain their posters and stories to each other.
Once this was done, I asked the pairs to sit down together for a quiz on what they'd studied. For this, I read questions about the two stories, and gave one point for the first pair to answer each correctly. However, within each pair, sea horse group students could only answer questions about the eagle picture and eagle group students could only answer questions on the sea horse story. In each pair, students could give the answer to their partners, but the partner had to announce the correct answer to me.
These are three examples of mixing environmental content with conversation activities. If you're interested in these ideas, I suggest you try them out and try integrating global issues into other activities.