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Reference requests are common. However, I wish to make this a list of books which every undergraduate, majoring in mathematics should own or at least read. It may be a bit subjective.

Please include 1 book per answer. If there is any additional (or alternate) recommendation by you or some other person for the same topic please include it in the comments.

I am flagging it for community wiki.

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    It got closed as $n$ot a real question but I voted as "not constructive" since everyone has their own opinion.2012-10-30

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Aigner and Ziegler, Proofs from The Book. Hours of fun.

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A bit clichéd, but...

Principles of Mathematical Analysis by Walter Rudin