It is possible to mine Bitcoin, Ethereum and other Altcoins without buying any specialist equipment.
To do this you purchase a mining contract from a cloud mining company and they run the rigs for you and credit you with the mining rewards.
Beware: Many of these companies have been dishonest and some just outright scams in the past so be very careful before buying. Also even if they are genuine, you pay upfront for a 2 year service so they could just go bust/insolvent.
Genesis Cloud Mining
If you want to test the water and give cloud mining a go then one of the longest standing and reputable companies is Genesis.