After 8 major releases of iOS, I still can't believe you can't reply to an email with an attachment. I need this for work and was the reason I switched to Android 3 years ago.
Apple should be embarrassed to leave out something so basic in 2014.
You can't really REPLY and paste an attachment because there is no mechanism to browse/copy/paste a file from another app.
However, you can certainly email attachments from third-party apps, amongst them are OneDrive, Evernote, and GoodReader. Dropbox apparently only sends links to Dropbox files, but if I had to attach one, I'd email it from GoodReader. I often fill out a document in Word or Pages on my PC or iPad, convert it to PDF and have a customer sign it on the iPad, then email it as an attachment.