No planetary nebulae visible with the naked eye? Think again. Granted, dropping NGC 7293 (Helix Nebula) there are not many observations of planetary nebulae with the naked eye. There are three other objects that are brighter than 8th magnitude: M27 (7.4), NGC 3242 (7.7) and NGC 7009 (7.9). With a little stretch you can add NGC 6752 (8.1), NGC 6543 (8.1), NGC 7662 (8.3) and NGC 7027 (8.5) to the bunch.
NGC 6543 should a great naked eye challenge and its location is easy to find. Not many confusing field stars.
NGC 6752 sits barely enough away from the Milky way and it might be possible to see with the naked eye, although probably more difficult than the Cat's eye (NGC 6543).
NGC 7009 is probably the easiest of the fainter ones. Easy to find, basically only two problematic stars in the vicinity (HD 200229 mag 8.2 and HD 200342 mag 8.4) although both of these more to the north-west.
NGC 7027 is in a very difficult spot - right in the rich fields of Milky Way. Considering its magnitude of 8.5, this planetary is probably invisible.
NGC 7662 is very faint and has several 7-8 magnitudes stars in the vicinity. Probably very difficult to identify. Watch out for magnitude 8.2 HD 220822.
This leaves us with two planetary nebulae that are well brighter than 8th magnitude.
Messier 27 - Dumbbell Nebula
This object stands boldly in Vulpecula between the rich Milky Way fields of Sagitta and Cygnus. It is not in the best possible spot for a naked eye gaze but it could be worse. Imagine the planetary 30° higher, hiding somewhere close to Deneb in northern Cygnus... then you'd be in real trouble. But as we know, the planetary is in Vulpecula and even better, the star fields are slightly less obvious in the region (compared to say Sagitta) and the area is not packed with many stars brighter than 8th magnitude. The triangle of 14, 16 and 17. Vul (or 14, 13 and 12. Vul, depending on how your averted vision works best) can be used to move your eyes around the M27 and see if you can pick it out with averted vision. Also the 7.7 magnitude star (HD 189733) W from our planetary should not be confused with the actual object. There are several stars around M27 making the field quite confusing.
Is Messier 27 really a naked eye object?
How many observing reports are there in the internet? Frankly just one. David Knisely has claimed seeing M27 with the naked eye sometime in 2001 from Nebraska Star Party site (3100 ft elevation, ZLM 7.5 to 8.0) but the details are lacking. I couldn't find any detailed, trustworthy reports on the Internet which of course doesn't mean there are none. It is also curious that O'Meara fails to mention this as an naked eye object in his book "The Messier Objects". I say curious since O'Meara has claimed to have been able to spot both M68 (7.3 magnitude) and M79 (7.7 magnitude) without optical aid. Both of these are close to M27's (7.4) magnitude but are also at a lower altitude making these two probably more challenging to see than the Dumbbell Nebula. So maybe O'Meara just failed to try this with the naked eye.
This or that Messier 27 should make a great challenge for those early spring mornings if you're up for it.
NGC 3242 - Ghost of Jupiter
Ghost of Jupiter is a small (slightly larger than 1') 7.7 magnitude planetary nebula in Hydra. With the bright magnitude and stellar appearance with the naked eye, this object is a fine challenge under pristine skies. Compared to the rich field surrounding M27, NGC 3242 is a piece cake. It sits quite nicely inside a square of 4 stars between magnitudes 6 and 7 and there are no real stars around here to be confused with the planetary itself. Stephen O'Meara mentions the planetary as a naked eye object in his 2002 book "The Caldwell Objects". I've observed this nebula myself, here are the details:
Observing less than a hundred meters from the NOT (Nordic Optical Telescope) in the island of La Palma at an altitude of 2390 meters (7840ft) I was able to spot the planetary nebula without optical aid on the night of 29th of March 2008. The weather was excellent despite the strong (16 m/s) winds and I recorded the evening as being one of the best (if not the best) of my entire observing career. The temperature was +3°C, humidity ~27% and seeing 0.8".
I did some observing with my 4.7" telescope while waiting for NGC 3242 to climb as high in the sky as it could. Slightly before 10 pm I located the 4th magnitude star Mu Hydrae and started to observe the area south of the star for the planetary nebula. I used a triangle of 6th magnitude stars in the region as guide stars while scouting the region. NGC 3242 is actually in the middle of this triangle. I spent about an hour in the area trying to detect as many faint stars as possible. After I was done with the sketch I took out my 8x30 binoculars and confirmed what I thought was 3242 with the pair of binoculars. I then compared all the 10 stars I had sketched with my Sky Atlas 2000.0 and surprise surprise one of these stars was indeed NGC 3242. I had marked two of the stars as the possible planetary nebula. One of these was 7.6 magnitude HD 90574 close to a 7.1 magnitude star HD 90606. I had marked this star as a possible double and it was. The other star marked was the planetary. There was a very faint, possible detection (blinked a few times during the entire session) of something in the southern end of the scouted region. This turned out to be a 8th magnitude star HD 89981. Here is the sketch made during that night. NGC 3242 is marked with an arrow.
Naked eye observation of NGC 3242 - Ghost of Jupiter