It's A Phase - this is a common reaction most noticeable to girls coming out as bi in teenage years. Sure, it might be true, but that doesn't mean it always is. People just jump to this conclusion, and it doesn't matter - they identify as bi now, so take them at their word.
Promiscuity/monogamy - Some straights/gays/lesbians believe that to be bi is to by definition have both a girlfriend and a boyfriend at the same time. Or that bisexual is just another word for someone who sleeps around with anyone that moves. We are capable of monogamy. There are those who cheat, those who have a lot of sex, and those who are polyamorous among us, but only in the same way that there are people like that who are straight or gay. It is not the default position with the bi identity.
All about sex - Captain Jack Harkness has not done a lot to dissuade this myth. Kinda the same point as about promiscuity.
Threesomes - classic conclusion, esp. straight cismen about female bis. Bisexuals are only in it for the threesomes. Again, there are some bis who do threesomes, some who don't, just like there are gays and straights who will or won't. Sure, in some ways we're more open to them, but that does not necessarily mean we're into them just automatically because we are bi.
Doesn't exist - some people (both gays and straights) claim there is no such thing as bisexuality. They say that those that claim to be are only either confused, indecisive, or taking the 'easy option' rather than come out as fully gay - “people are either gay, straight or lying”. It's just plain factually incorrect. There is scientific proof of behaviour and physical arousal, as well as a community of people who identify as bi. If someone tells you they identify as something, you have no right to tell them they're wrong about themselves, none, no matter who you are - your parameters for what sexuality, or any other identity, is are not what counts; they identify, so you believe them. And that might change; doesn't matter - if they take on a new identity, you take them for that, without judgement on the change, or trying to know the details.
Greed - it's either said as greedy or slutty. It's kinda like saying bisexuality doesn't exist or promiscuous, bisexuals are just people who want any option. Well, no, we're as likely to be desirous of sexual or romantic involvement as anyone is likely to be - it is independent of our orientation. It's our nature to like more than one but that doesn't necessarily mean we want any more romantic or sexual activity as anyone else.
Equal attraction - this is an interesting one. I say that because I am in fact myself equally attracted to the two ends of the spectrum - within the bisexuality umbrella, I identify as bisexual. But this is not often the case, as is the misconception. A lot of straight people seem unaware that bisexuals often have a preference of one gender over the others, whilst still being attracted to all of them, or of the identity within the umbrella of pansexual, where gender has no restriction on attraction.
Two competing natures - "Bisexuality is not a combination of heterosexuality and homosexuality. We're not half formed or half committed. We're whole. We are not bi-sexual, we're bisexual!" - The Bisexual Index. The umbrella of identities that is bisexuality is the third option, because there are more than just gay and straight!
Continual alternating - when we're with the same sex, we're gay, with the opposite, straight. We aren't bi, we just go back and forth between the two. See 'two competing natures' and 'doesn't exist'.
Everyone is ultimately bisexual - this is the most controversial, brought to light especially by Kinsey. I'm not a huge fan of the hypothesis, but I won't rule it out entirely. Essentially, this is the theory that everyone, even if they claim to be straight or gay, is ultimately bi. Look it up and make up your own mind. Many people who identify as bisexual don't believe it, and feel it is detrimental to fighting biphobia to promote the idea.