A few thoughts...
ZIWA (Zürich International Women's Club) is often needs volunteers to help with various things - and the club uses English as it's working language. The club is mainly activity based, but they also choose a charity to support each year for which they hold a variety of fundraising events.
(When we first moved here I joined as a way to find my feet and meet people. I'm not very active anymore, but the friendships last... )
You might want to look into joining any of the international clubs, or a local
Verein catered to your interests (sports, hobbies, etc.) if your German is decent.
Other ideas:
WWF and Greenpeace and other environmental groups (like your local Wald- or Naturschutz group) regularly need volunteers, even if your German isn't great there are generally things to help with.
And most animal welfare groups need help... the critters will understand you whatever your language skills.
How about the local
Altersheim (Senior citizen's home)? Many residents know English, and may enjoy a visit from an English speaker...
The umbrella organization for senior citizens is Pro Senectute:
http://www.zh.pro-senectute.ch/
How about the Red Cross?
http://www.redcross.ch/activities/vo...s/index-de.php
While the ZH office mostly asks for German speakers, why not offer your skills and see what they say?
And if you live in a small-ish town, why not talk to the
Gemeinde? The folks there often hear of opportunities, formal or informal, where you could be of help.
And, check out the volunteer job bourse:
http://www.freiwilligenjob.ch/c/Frei...9/Default.aspx
(You'll need German for most of these, however if there is an organization that interests you, why not contact them and offer to help in another capacity?)
There are endless organizations needing volunteers. Any charity that interests you would be worth contacting. Most can always use a pair of willing hands, regardless of language skills. - often you just have to call and ask how you can help.