I'm trying to put together the following circuit (part of a serial programmer for an ATiny13) but I don't have any 27pF caps. I do have 22pF and 33pF, would either of those be suitable replacements?
Generally, yes, it is OK to substitute them. Those capacitors are used to pull-down the crystal to help it start oscillating. In some cases, you can even omit them, but not for reliable operation. You have to check the crystal's datasheet for recommended capacitors, and the microcontroller's datasheet will often specify a range as well. For example PICs usually support 15pF to 33pF for the capacitors in the XS (high-speed crystal) mode.
I just checked the AVRs datasheet, turns out it doesn't even use a crystal (the circuit is for what I _thought_ was a pin compatible ATTiny12). Glad I didn't solder the crystal on yet