This is helpful for infamous characters (although you could also just complete the Pilgram's Way). Transcendent Sigil Stones start appearing at level 17. At the highest levels, the Transcendent Sigil Stones offer the best enchantments in the game.
There are two reasons why you should make it a practice: You can close them, of course, but it isn't easy.
But since the Emperor died at the start of the game, and the Dragonsfires are dark, they can now be summoned. Oblivion gates are a staple in the Main Quest, and according to Martin, the portals shouldn't be possible. It looks very evil, with lava (which you can swim through or use a Water Walking Spell on, although it rapidly damages your health), Daedric creatures, and even plants that fight back! Oblivion Gates are portals of some kind to Dagon's realm of Oblivion.