There are a number of situations where the sale of an asset is exempt from CGT. The corollary is that if a loss is made in such a situation, it cannot be offset against other gains.
There are two main situations in which an exemption is given.
1. Gifts to the state or family
As a general rule, the proceeds for the purposes of capital gains tax is the value of the asset, even if it is gifted. However...
Gifting an asset to the State of Isrsel or one of the bodies associated with the State (e.g. KKL or UJA), or to a public organisation (i.e. charities) are exempt from CGT.
Also, gifts given to family members are exempt from tax. It should be noted here that family is defined as ISRAELI spouse/(grand)parent/(grand)child/sibling and their respective spouses. Non-Israeli family members do not fit into this category.
That being said, the tax authority can also grant an exemption for a gift given to someone else if they can be persuaded that the gift was given legitimately (and not as a tax ruse).
2. Oleh Chadash
Anyone who made Aliyah, or is a veteran returning resident, after 1st January 2007 has a 10-year exemption on capital gains tax when selling assets that are not located in Israel. It is irrelevant when the asset was purchased. After the expiry of the 10 years, the total profit is divided by the total number of days that the asset was owned for and only the number of days-worth of gain after the expiration of the 10 years are subject to tax.
For anyone who made Aliyah in 2006 or earlier, or is a non-veteran returning resident (even now), there is a 10-year exemption when non-Israeli assets are sold. However, the caveat here is that the exemption applies only to assets owned before moving to Israel. The tax on gains made after the expiration of the 10-year exemption is the same as above.