How do I connect a 555 timer to a CMOS Input?
If you run the CMOS from the same supply voltage there should be no problem in directly connecting the 555 to a CMOS input.

The TTL chips are pretty much limited to a supply of around 5V +/- 0.5V. This may be an issue. If the 555 is running from a 5V supply they can be directly connected as the output of the 555 is both source and sink (sink being required for TTL input)