Who is a vaishnava?
Saying "someone who worships Lord Vishnu" is like saying a Christian is someone who goes to church. The answer's technically correct, but it doesn't distinguish between those who are nominally Vaishnavas and those who are truly Vaishnavas (or Christians).
An old song, called vaishnava jana ("A vaishnava man") by the Gujarati poet and saint Narsi Mehta contains a much better answer to the question. The song was Mahatma Gandhi's favourite, and I think it's the best definition I've ever seen of what it means to truly believe. Here's the text, with my (rather free) translation:
vaishnava jana to te ne kahīe je pīda parāī jāne re
paradu:khe upakara kare toye mana abhimāna na āne re
sakala lokamā sahune vande nindā na kare kenī re
vācha kācha mana nishcala rākhe dhana dhana jananī tenī re
Call him alone a vaishnava, who feels the suffering of others as his own
who helps those in need, with humility, without pride,
without the desire to earn the world's praise, and without condemning those who do less
whose mind and words are steadfast, who is a wealth beyond wealth to his homeland;
samadrshti ne trshnā tyāgī,
parastrī jene māta re
jihvā thakī asatya na bole
paradhana nava jhāle hātha re
who has renounced arrogance, whose conduct is the same towards all,
who behaves towards all women as he would to his mother
who walks in the ways of truth,
whose hands and mind are not stained by covetous desire;
moha māya vyāpe nahi jene
dhrda vairāgya jenā manamā re
rāmanāmashun tālī lāgī
sakala tīratha tenā tanamān re
who is not driven by passion or material wants
whose mind is filled with the spirit of renunciation
whose heart and mind exult in the glory of God,
he needs no pilgrim's garb, save his body and his thoughts
vanalobhī ne kapatarahita che
kāma krodha nivāryā re
bhane narasaiyo tenu darasana karatā
kula ekotera tāryā re
who is neither avaracious, nor vile
who is free from lust, and free from anger.
I, Narsi, long for the company of such a man
for in his presence, we shall be free.