Selling:

Capital Gain Tax — is the tax you have to pay for the difference between what you sold the property for and what you paid for it discounting the expenses you had on the transactions and investments on the property (if you are a non resident in Spain, the buyer has to deposit 3% of the purchase price at the Tax Office to cover for this tax or other non paid taxes in Spain. A tax declaration of the sale has to be presented by the seller to liquidate that tax where the 3% retained will be accounted for: if the tax is higher than the 3% the seller will have to pay the extra but if the tax is lower the seller will get a refund). There are also special cases when you are over 65 years.

Plusvalia Tax—Payable to the Council to account for the increase of value of the land where the property is. The amount is calculated by multiplying the catastral value of the land, the number of years of ownership of the property and two more coefficients that depend on the Council.
Additionally and independently of the taxes, you can download a cheat sheet here to calculate your net after discounting all the cost associated to the sale: Net Sheet Page

Buying:

Transfer tax or VAT (plus AJD) — I have written some articles about this because there are some different cases depending on the type of property: residences, land, garages, storages or commercials. In general, if it is a new property it will pay VAT (plus AJD—an additional 1,5%) ranging from 10 to 21% of the purchase price and if it is a second hand property will pay transfer tax ranging from 8 to 10% of the purchase price.

Notary and Land Registry expenses (although they are not really taxes are payable on each transaction).

Owning:

I.B.I. tax — it is payable to the Town Hall to pay for the maintenance expenses of the Council. It is calculated from the catastral value of the property.

Rubbish collection tax—it depends on each municipality and in some cases is also calculated from the catastral value of the property.

Wealth tax—this tax may be complex so if you are a resident in Spain is advisable to have a tax advisor.

Rental income of non residents—whether you are renting your property or not, the Tax office will require non residents to pay this tax. The base for the tax is also calculated from the catastral value.

Since each particular case is different, it is fully recommended that you check your own details with your lawyer or tax advisor.