After looking around for a set of rules to play games of WW1 that do not include 5 different steps to complete a single action (exaggeration, of course) in a single turn, I found this rule set.
The game is a 'Fast Play' system. The book has 19 pages in total and all of that is dedicated to the games mechanics which are all fairly simple and straight forwards, though there were certain elements I personally needed clarified by the author who was more than happy to help.
Unlike most WW1 based games I have seen that use cards for most of the basic actions, this game uses a simple D10 roll and comparing it to the units stats. This simple system works in all aspects of the game (unit Activation, Shooting and Melee)
Inititive and unit activation works on a modified "You Go, I Go" system, where one player rolls to activate a unit and if he succeeds the player can continue to roll and activate another unit in the army until a failed roll, then the inititive is given to the opponent who activates his units one by one until he fails to activate a unit, then the inititive moves back to the first player, and so on until all units are activated that turn.
I feel this system is perfect for simulating the changing nature of Trench and modern warfare where the initive can easily be lost at any moment.
The only issue I have with this book is that there are no stats, or army lists for the main combatants of the war. Those can be found in the companion book "1916: The Year of Slaughter."
While the book was designed for WW1 specifically, there is nothing to stop others from using this as a basis to play other periods either before or after WW1. The rules are quite adaptable to most periods during the gunpowder era (1700 - 1945). They may need a little bit of house ruling, but it is possible.
All in all, a very good set of rules and I would recommend at least giving the rules a look through. The companion books adds historical scenarios that can be played, or you can play a simple objectives based game that simulates the more mobile aspects of the early war and end of war periods.