All French verbs take 'avoir' to form the passé composé tense except for these seventeen verbs:
aller, arriver, descendre, devenir, entrer, monter, mourir, naître, partir, passer, rentrer, rester, retourner, revenir, sortir, tomber, and venir,
which take être instead of avoir.
All pronominal verbs (se lever, se coucher, se promener, etc.) also take être instead of avoir to form the passé composé tense.
Just a few details about those of the 17 "être" verbs which also exist with "avoir" when transitive:
- Descendre: j'ai descendu l'escalier (I walked down the stairs)
- Descendre: il a descendu son ennemi (he shot down his enemy)
- Monter: j'ai monté l'escalier (I walked up the stairs)
- Monter: j'ai monté la mayonnaise (I wounded up the mayonnaise)
- Entrer: j'ai entré mon mot de passe (I entered my password)
- Passer: j'ai passé des heures à travailler (I spent hours working) + many, many other uses
- Retourner: j'ai retourné la crêpe (I turned the crêpe over)
- Sortir: j'ai sorti le chien ce matin (I took the dog out this morning)
- Tomber: j'ai tombé la veste (I took my jacket off)
That's the way I was taught them too. For what it's worth, I was taught to use the mnemonic ADVENT:
Arriver (opposite is partir)
Venir (aller) [and this is the point to remember devenir, revenir]
Entrer (sortir) [and remember rentrer here]
That way there's only a few stragglers to remember off by heart. I may have remembered this all slightly wrong, but the fact I've remembered it at all ten plus years down the line suggests it might be of some value.
There also seems to be a pattern about motion with these verbs. Most obviously: coming, going, leaving, descending, etc. (as well as all the verbs based on venir). Rester has to do with stopping motion, so it sort of fits. The only ones which don't seem to fit this pattern (I think) are mourir and naître. But think of these as entering and leaving life, and they still fit.
New learners--the être verbs can be remembered by an anagram, "DR. MRS. VANDERTRAMPP"
Montrer Retourner Sortir
Venir Aller Naître Devenir Entrer Revenir Tomber Rester Arriver Mourir Partir Passer
In addition, in high school, we wrote & drew on a picture of a house and thought of all of these verbs as things you do with the house--go up the stairs, go downstairs, leave it, come back to it, etc. We would be "born" into the ceiling above it and "died" in the soil. Weird, but it worked.