Most of the terminals seem to use copy on select and middle-button to paste selection, or emulated middle-button to paste (using both mouse buttons at once). This is typical Unix behavior, and the emulation is the updated usage required by Microsoft-type mice with only two buttons or two buttons and a scrollwheel.
The mouse buttons could be remapped with xinput or other means. This will differ from version to version and on different mouse models. See the Ubuntu community documentation for that.
Also see this question, which is the reverse of the procedure you'd need.
Terminals I have that use select to copy and middle to paste include Gnome terminal, xfce terminal, Eterm, plain xterm, uxterm, rxvt, mrxvt, and aterm. I'm sure there are others.
My primary terminal, terminator (use apt-get or the software center to install), lets you choose copy on select as an option (with a single click):
Open preference and click the 'copy on select' box :