At my day job, we have landline phones that break a few times a week. It's a big organization. Anyway, I was horrified to learn that instead of our engineers fixing the phones, I was told to throw them away instead. With the popularity of cell phones, I'm sure that landline phones will eventually be obsolete.
I couldn't believe how few recycling programs there are for landline phones. I mean there's a million recycling programs that take cell phones which is great. Part of the problem is the plastic used for many regular phones isn't recycleable.
I read that Best Buy will take old cordless phones and recycle them.
Staples will take your old landline phone and you get a discount to buy another one. http://www.staples.com/sbd/cre/products/110508/merch12185/index.html
Donate to charities who can use the phones for fundraisers or their office. Also thrift shops might take them as well.
Lastly, check out your local municipality to see if they will take landline phones. Many will have electronic recycling drives a few times a year so be sure to find out when the next one is.