We have registered cattle, and I'm adamant about everybody's tag matching the tattoo. That just makes things so much easier when you're matching up papers or doing your record keeping. We use the year letter designation because it's required by our breed association for permanent ID, and I like it because it gives you 22 more characters (not using I, O, Q or V). Years ago, my dad started assigning new numbers to daughters of cows in the herd, but his system was never consistent & I don't like losing track of cow families. Nowadays, most of the calves will have two letters...their own year letter, then the cow famy number, then the dam's year letter. That tells us what year the animal was born, who the mother is, & how old she was when she had that calf. So a calf born this year might be Z81U...Z for 2012, 81 is the cow family, and the dam's year letter is U. We also have a Z81S, so we know those calve are born the same year and out of maternal sisters. The trick to this system is incorporating the year letter designations and using them as part of the ID. We can't just call one "#9" without remembering the letters, but you get used to that. I like it a lot better than random numbers, and I don't think it's any more complicated than systems with more than one number to try to keep up with all that information.
I also have some Angus cattle, and the heifers I kept there a couple years ago got 10 numbers that related to their dam's numbers. Angus doesn't require the year letter, so this heifers are 1040, 1097 & 1087, and I can remember they were born in 2010. I just had to make the numbers correspond with the dam numbers though...it isn't a consistent system for doing that. Their mothers are 540, 597 & 8705. I could explain the reasoning there, but there really isn't any point. You just have to do what works.
I don't mind the system of Z101, Z102, Z103, etc. But you have to have good records to keep up with what calves go with what cows. I find it easier to keep up with things and to know the cattle when they keep their "family number"... Kinda like having a last name.