Not to do with mIRC, but in relation to the nag-ware topic, I think that the free software available from dqfree.com
(looking specifically at their 100% Free Euchre and 100% Free Five Hundred games) have a far more naggy (if that's a word) pop-up. It shows up after about every 4 or 5 hands in a game.
Personally, I don't mind the free versions, but I don't like them enough to upgrade to the paid versions. In addition to the nag screen, there are a number of options that are selectable, but not usable in the free version, and if you try to use them, you get another "nag" screen stating that the item you tried to use is only available in the Pro versions.