Electrical – Replicate PCB design on stripboard

Fritzing looks like the ideal tool for this:

• Free (GPL license)
• Multi platform (Linux, Mac OS, Windows)
• Integrates a large library of components

The stripboard can be resized, you can chose the strips to be vertical or horizontal. You can also cut the contacts with your mouse like you would do in real life.

Example circuit:

Edit 30/10/2018: Make sure you add a Stripboard and not a Perfboard, the Stripboard is the one circled by the dark red square on the following screenshot: (third item on the first row)

First, you don't need to do home PCB etching to get real circuit boards made. BatchPCB and other prototype services can get you real, quality PCBs for (sometimes much) less than $50. If it's just for a temporary project, solderless breadboards are also a great tool. I will admit, however, that some projects fall into the middle of these categories.

Usually, I just poke the components through .2" graph paper for checking that an imagined layout will work. This seems to work well enough for most of the simple circuits that I make on perfboard. If you want to use Eagle PCB, configure the layout editor for 0.1" grid spacing, and display the lines:
Now you can lay it out on a model of your stripboard. You might even want to diagram the strips. Use the "Draw Lines" tool on a non-copper layer (like Documents) to avoid confusing Eagle with respect to electrical connections. Record where the strips should be left intact on one layer, and make wire jumpers on (an) other layer(s).

After that, it's up to you to create an intelligent layout. Since these kinds of boards are usually for development purposes, make it spacious and easy to understand. I try to organize power busses with higher voltages at the top and ground at the bottom, route signals from left to right, color-code connecting wires (esp. if you're not using stripboard), and provide lots of room for edits to fix the mistakes I know I will make. I also like to keep my components on one side and route wires on the other even when using double-sided board.