I remember them being in CL every year, often shocking the big names like Milan, Barcelona, United and Bayern. Wasn't it Ravelli's team? When I hear his name his celebration during a game in 1994 World Cup comes to my mind, when another attempt of Brazil to score just failed... Found this video, around 3:20 there is the scene that I mean. Watching the whole thing is worth it, some great saves:
Different, in my opinion better times when there was not such a huge gap in quality between the teams and leagues. CL quarterfinals Bayern vs IFK Göteborg was 0-0, 2-2 back then and I remember Bayern players celebrated in the bus singing their coach Giovanni Trappatoni's name to the melody of "Vamos a la playa" as they made it to the semis thanks to the away goal rule... and then the young Ajax of van Gaal demolished them 5-2. Tell that to young fans and they will probably not believe you. Luckily they can google it

At least we see a strong Ajax again these days, but of course not the same level as in 95 (or the 70s I guess, wasn't born back then).