Openings that keep the king in the center on purpose? Discounting cheap tricks to mate in only a few moves. Are there any serious openings that keep the king in the center with no intention of castling?
There are many respectable opening lines where the king stays in the center. A popular opening at the highest level is the Berlin Defense:

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1. e4 e5 2. Nf3 Nc6 3. Bb5 Nf6 4. O-O Nxe4 5. d4 Nd6 6. Bxc6 dxc6 7. dxe5 Nf5 8. Qxd8+ Kxd8