The short answer is yes. Most of my relationships are without sex (friends are technically relationships), though if you mean romantic relationships it becomes more complicated.

As to whether you can have a successful romantic relationship without sex, I suppose that depends on what you mean by "successful." It also depends on how you both feel about it.

If one party wants it and the other one does not, then in a monogamous relationship it can be very difficult to maintain the relationship for a long period of time. If the relationship is purely platonic by mutual consent, then is it really a romantic relationship? (this is a question with an answer that only is true within your individual frame).

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"'Love' is that condition in which the happiness of another person is essential to your own... Jealousy is a disease, love is a healthy condition. The immature mind often mistakes one for the other, or assumes that the greater the love, the greater the jealousy. " -- R. A. Heinlein