Your ticket always includes a carry-on bag (55 x 40 x 20 cm, 10 kg) plus a handbag or laptop bag.
When travelling to North America, you don't have to limit yourself and can take two checked bags up to 23 kg. For trips to Iceland only, you can check in only one.
Skis, golf bags or hockey equipment can be checked in as one bag free of charge (so in the case of a flight to the USA, you have one normal suitcase up to 23 kg + one sports equipment).
Unfortunately, as of autumn 2017, the baggage policy is moving towards low-cost airlines. Checked baggage is not included in the base fare. If you want to buy it online, you will pay €71 one way from Europe to North America, and that's not worth it. If you plan to travel with checked baggage from the start, buy the more expensive "Economy Standard" fare directly from the airline's website. Compared to an additional purchase, you will save €20-25 one way.
Icelandair carries pets for a fee of 126-174 usd depending on the distance.