Since I came from the US, I am more familiar with the Hueco Grade System (V-Scale), but since moving the Europe, I have run into other grading systems. The most common other grading system I encounter here is the Font Scale.
These systems both have a fairly clear scaling as the grades increase and get harder to climb. Personally, I find following the V-scale easier since each level increases by one grade where the Font system has multiple tiers for each grade level.
Hueco Grade System (V-Scale)
The Hueco Grade System is a system used to rate the difficulty of boulder problems (short, challenging routes that are typically climbed without a rope) in the Hueco Tanks State Historic Site in Texas, USA. The system uses a combination of letters and numbers to indicate the difficulty of a problem, with "V" being the highest and easiest, and "V16" being the most difficult. The system is considered to be one of the most challenging grading systems in the world, and many of the problems rated V13 and above are considered to be some of the hardest boulder problems in the world.
Fontainebleau Grade System (Font-Scale)
The Fontainebleau Grade System is another system used to rate the difficulty of boulder problems, specifically in the Fontainebleau forest in France. The system uses a combination of numbers and plus signs to indicate the difficulty of a problem, with "1" being the easiest and "8A+" being the most difficult.
The Hueco and Fontainebleau grade systems are considered to be two of the most challenging grading systems in the world. However, the Fontainebleau grade system tends to be slightly less difficult than the Hueco grade system. For example, a problem graded V13 in Hueco would be around 8A or 8A+ in Fontainebleau. This is because the rock in Fontainebleau is generally considered to be less difficult to climb than the rock in Hueco Tanks.
I found this handy guide that helps to make it easier to compare the scales of each system. This has helped me to better judge my abilities when climbing different problems as I am able to compare 1:1 verses the scale I am more familiar with. I keep a little printout of this in my gear bag just in case.
It's worth noting that different climbing areas have different types of rock and different climbing styles, so a climb that would be a V13 at Hueco might be a completely different type of climb at Fontainebleau.
There are many other climbing rating systems out there, but these are 2 of the most common I have encountered. What do you use to grade your climbs? Do you use any other systems?