I understand where this is coming from, but...honestly, I can't think of many games I've played even semi-recently that suffer from it.
There's, uh...Symphony of the Night, and that was the PSP version by way of The Dracula X Chronicles, so when you reach the true end you unlock more stuff. Most of the post-SotN Castlevania games do something along those lines, and on the other side of that coin, Metroid games since at least Super (I haven't played M2) mark a completed save file.
Most arcade shmups and ports of such list your stage completion on the scoreboard as "ALL" or some variation thereof if you finish the game, and shmups developed for home consoles to start usually have some sort of unlockables given for game completion in addition to that (usually more game modes, or things like Gradius V's edit mode).
The RPGs I've been playing all mark for completion and/or have New Game Plus-type modes.
Thinking about it, all of these are Japanese games. Aside from VVVVVV and Super Meat Boy, which do track a completed game, the only western games I've really been playing recently are strategy games like Civilization IV and AI War, both of which are the sort of game where tracking completion would be silly (and AI War has achievements anyway).