I once heard we should pay homage (bending, prostrating or some similar) to our parents on their birthday. If that is correct, for who else should we pay homage/bend to? Monks and parents only?
From a Therevada perspective, in the Sigalovada Sutta (Pali Canon) the Buddha says to Silaga that parents should be worshiped. He doesn't actually specify monks in this sutra as at this point the Buddhist monastic community wouldn't have taken shape. However he does specify teachers and also ascetics and brahmans so we can maybe take this as the nearest equivalent.
In total he advocates the worship of 6 groups of people corresponding to the 6 directions so
- Parents as the East
- Teachers as the South
- Wife and children as the West
- Friends and associates as the North
- Servants and employees as the Nadir
- Ascetics and brahmans as the Zenith
I have to say though he doesn't restrict the homage to their birthdays only. Sigala is portrayed as doing a daily practice of homage in the six directions to which the Buddha is responding.
From a Mahayana perpective, the Ullambana sutra the Buddha advocates paying homage to parents
Every year, on the fifteenth day of the seventh month
so this would be at least annual homage which is nearer to your question. In addition there is also the Sutra of Filial Piety which goes on at length about the trouble your parents have gone to to raise you (which is fair I guess - they have gone to a lot of effort). This is probably as influenced by Confucianism as much as Buddhism.
There are more of these type of sutras in Mahayana traditions but I'm already past my level of expertise so I'll leave those for other people to detail.
"From a Therevada perspective, in the Sigalovada Sutta (Pali Canon) the Buddha says to Silaga that parents should be worshiped".
Lord Buddha did not say that parents should be worshipped in the Sigalovada Sutta.
What the Lord said was that one should have 'anukampa' for the six categories mentioned. Anukampa may be translated as empathy; it is mutual.
Parents have duties--bringing children up; giving them an education etc. Children have duties--primarily looking after the parents in their old age, when they are feeble.
'Parents should be worshipped' is a complete misinterpretation of the Sutta. It changes one of the most fundamental concepts of Dhamma--Equality of all beings.
Sabbe Satta Bhavantu Sukhitatta.