Leon against West Germany in 1970 is still the worst. At the risk of sounding all Nick Hornby about it, the first time your heart gets broken is the one that sticks with you forever, and I've certainly never forgiven the Germans. 2-0 up, then Bonetti lets in a couple of duffers, Ramsey gets his substitutions all wrong, and Gerd ****ing Muller finishes us off in extra time.
More recently, losing on penalties after failing to see of a thoroughly moderate German side in 1996 hurt because it was such a wasted opportunity to actually win something. Ditto losing to Brazil in 2002. Although in that WC, we'd have probably lost to the Germans if we'd reached the final anyway.
Worst experience at club level was Palace's 1993 relegation. Did a lap of honour after winning our final game only to be overtaken by Oldham's games in hand. Final game of the season saw us at Arsenal, where we always got spanked, with Oldham needing to see off Southampton. IIRC Le Tissier got a hat-trick but Southampton conceded four, whilst we did what we always did at Highbury.