You're standing in the entryway of your apartment building, glancing at the utility bills you've just taken out of your mailbox. You see your neighbor step out of the elevator, but before you have a chance to say hello, he steps backs into the elevator and pushes the button of his floor. As the doors shut, he shrugs his shoulders and says sheepishly: Склероз! (Sclerosis!)
In this context, склероз is short for старческий склероз мозга (senile dementia) and more specifically refers to one symptom of the disease that typically affects people as they grow older: memory loss. So when your neighbor, the dapper old Артур Иванович, saw you at the mailbox, he suddenly remembered the bills he'd forgotten to take with him. His twin in a Florida retirement home would do the same thing and say: I'm having a senior moment.
In English, sclerotic can be used figuratively to mean something rigid and unchanging, usually an institution, like a parliament or organization: "The EU is sclerotic, hopeless and downbeat," one leader said before the Brexit vote. But in Russian, you'd probably only call the parliament склеротический (sclerotic) if you meant old and slightly demented, not tradition-bound and rigid.
Russians have a lot of jokes about склероз, which have a slightly whistling past the graveyard quality to them: У меня та самая болезнь, названия которой я не могу вспомнить (I have that disease whose name I can't remember.)
Of course, you can forget things at any age. You might be called забывчивый (forgetful), which might be a minor nuisance for the "little woman" — and provide a good marketing angle: Забывчивым хозяйкам очень подойдет чайник, подающий сигнал при закипании (A tea kettle that signals when the water comes to a boil is just the thing for forgetful housewives.) But general amnesia might be a big problem for humanity "Прошлое всегда подстерегает забывчивых современников," — предупреждает автор в конце своего труда ("The past always sets traps for forgetful contemporaries," the author warns at the end of the book.)
Забывчивый is a bit different from невнимательный (inattentive), although someone who pays little attention to things will probably forget them. Он настолько невнимателен, что оставлял работу дома на столе, а иногда шёл по дороге и вдруг останавливался, не зная куда он собирался (He was so absent-minded that he'd leave work at home on his desk, and sometimes would be walking down the street and stop because he didn't know where he was going.)
This kind of general forgetfulness is also described as рассеянный (absent-minded), what professors and old folks are: Он человек довольно рассеянный и неаккуратный — ему случалось нечаянно портить оборудование или терять нужные бумаги (He's rather absent-minded and careless. He has ruined equipment by mistake or lost important documents.)
Sometimes you aren't generally forgetful, but something just slipped your mind: Ой! Я совершенно забыла нашу встречу сегодня! Она просто вылетела из головы! (Oops! I completely forgot our meeting today. It just slipped my mind, literally "flew out of my head.") У меня дырявая голова (My mind is like a sieve.)
There may be more expressions, but I've forgotten them.