Why do some verbs take 'etre' in the perfect tense? And how can I memorise them?

The majority of French verbs are take a conjugated form of the verb 'avoir' (to have) when forming the perfect tense, similarly to English. However, there is an important minority of verbs that use a conjugated form of the verb 'etre' (to be) when forming this tense. These verbs are called intransitive verbs, meaning that they do not take a direct object. These verbs often refer to a change in state or place, and although there aren't many, they are very important! 

For example;
J'ai vu la montre - I've seen the watch (watch = direct object)
Je suis descendu - I went down (no direct object) 

Fortunately there's a nice trick to memorise these verbs. All you have to do is meet MRS VAN DER TRAMP, the agreable Dutch lady who never objects! 

Monter --> monté (went up)
Retourner --> retourné (returned)
Sortir --> sorti (went out)

Venir --> venu (came)
Arriver --> arrivé (arrived)
Naître --> né (was born)

Descendre --> descendu (went down)
Entrer --> entré (entered)
Rester --> resté (stayed)

Tomber --> tombé (fell)
Rentrer --> rentré (went back in)
Aller --> allé (went)
Mourir --> mort (died)
Partir --> parti (left)