The file the chats are in is /data/data/com.skype.raider/files<yourscreenname>/main.db. It's a SQL file. If you back that up (the phone has to be rooted to get to it), you'll have a backup of the last 3 months of conversations (or whatever is saved on the phone).
If you copy it to a PC and use a SQLite program to access it, you can join multiple backups into a single file, extract all the conversations, conversations in a particular date range, anything you can do with a SQL database. (You'll probably have to learn a little SQL though - there's probably no program written specifically for that file's format. I haven't even been able to find a Windows program specifically for that file. But there are SQLite programs that read and manipulate SQLite database files for both Android and Windows.)
As far as ICQ, it's about the same process - search the web for file information. In an Android phone, it's most likely to also be a SQLite file.
Maybe someone can convince Skype to add a "backup up my conversations to a text file" function.