How can I remove myself from a group text message thread in iOS?

I have friends that like to text large groups of people and I'm basically subject to repeated messages of various people responding.
With email it's different - email is much easier to ignore.

Unfortunately you can't - unless they are using a special app or service (GroupMe comes to mind).  If someone adds you to a group list that is being generated on their personal device you can remove others from a reply that you send to the group by simply deleting their name/number from the "To:" field but if someone replies to the entire group you're going to get whatever they send. 

Functionally it works the same way as an email - one you're in a "Reply All" loop you're stuck.  That's why it's essential to use the "Bcc" field in emails when sending to a large group (just address the email to yourself and put everyone else in the Bcc field) - that way if someone hits "Reply All" there's no chance of it going out to everyone. That option doesn't exist in the native iOS Messages app.

Of course, you could do what I do when someone puts me on one of those group lists: I text the person that sent the original message to the group saying, "Don't even THINK of putting me on one of these group lists in the future."