The most memorable one I can think of was in How To Be A Complete Bastard.
On you quest to ruin a party & be a complete bastard to everyone you come across a computer in the hallway. One of your options is to switch the computer off/unplug it, but if you do it resets your computer, and in the case of the Spectrum I played it on, meant having to load & start the game again.
Not the most rewarding secret, but still great nonetheless, mainly due to it's innovation.
I also fondly remember all the funny secrets & jokes on Summer Games on the Amiga. Most of them involved failing your attempt at an event, but were funny.
Shooting the ground in Archery would make a mole appear & say "Hey man I don't dig that!"(?)
Firing an arrow into the trees in the background during archery would result in a scream.
Messing up during the hammer throw would result in a smashed screen or your compeitor being launched out of the circle with the hammer you didn't let go of.
Waiting in the pool after a diving attemt would trigger a sharks fin to appear & Jaws music to play.
On the menu screen in North & South, clicking the pointer on the photographer's arse would make him giggle & move.
IK+ had lot's of little secrets too, such as pressing T to make the fighter's trousers fall down, typing swear words & being reprimanded, pac-man & periscopes moving through the background...
I don't know, but in the old days of games, little secrets like these seemed more novel & better thought out, more subtle. Now it seem obligatory for games to have easter eggs, no matter how meaningless & taped on they are.
The only recent "easter egg" that stick out on my mind, is the secret "Volition offices" level in Summoner, where you were warped to the real world & could chat with Volition staff.