Krakow, and especially the Old Town, is a centre for various events such as exhibitions, concerts and festivals - organised for the locals and tourists visiting Krakow. Some of the events are occassional and take place only once while the others are organised annually.
Many of the events are organised by Krakow Festival Office.
You are mostly advised to attend annual events:

Welcoming of the New Year - each year the city organises one of the biggest open-air party in Poland on the Main Market Square in Krakow. The night is full of concerts (also international performers are invited) and the locals share the joy of welcoming the New Year with all the visitors to the city.
Carol Songs concerts in Krakow churches - as the tradition of singing Carol songs is very vivid in Poland, some concerts with traiditional carols are organised in Krakow churches. By listening to them you may hear to Polish traditional music.

International Festival of Sailing Songs ("Shanties") - the festival features Polish and international singers of sailing songs. Its official website is unfortunately only in Polish.

March / April:
Easter Tradition in Krakow - Easter Holidays are full of customs: typical for Poland or only for Krakow. Traditional events, taking place in the city, fill the period of Easter Holidays and are open to all the visitors.
Misteria Paschalia Festival - the festival takes place parallel to Easter Holidays and features variety of concerts of historical music. On the official website you may find detailed programme and gallery from previous editions.

The Night of Museums - during one May night all of Krakow museums are open till late night and present special events to attract the visitors. The entrance ticket costs symbolic 1 zloty and allows you to visit all of them.
International Soup Festival - musical event that is joined with a contest for the best soup. Each year the festival takes place in Kazimierz district.

Floating of the Wreaths  - the shortest night of a year will be celebrated in Krakow by traditional Polish midsummer festival taking place along the Vistula river bank (concert and artistic show will be ended by fireworks). On the website of Krakow Festival Office you may find gallery from previous year.
Jewish Culture Festival - the festival is filled with concerts, workshops and exhibitions (all referring to Jewish culture). On the official website of the festival one can read about its mission statement and see photo galleries.       

Traditional Music Festival "Rozstaje" - the festival features performers of traditional music from Eastern Europe. The official website is unfortunately only in Polish.
Summer Jazz Festival - the festival is held in "Under the Rams cellar" and offers jazz concerts performed by intrernational stars. Official website provides information on detailed programme and the festival itself.         

Pierogi (Dumplings) Festival - dumplings are very popular in traditional Polish cuisine. The festival gives the opportunity to get to know this tradition better as well as to try out Polish specialties.

Sacrum Profanum Festival - the festival presents masterpieces of vocal and instrumental music in geographical order. Official website offers more information about this annual event.    

International Festival of Old Music - the festival presents works of old music, played on old, traditional instruments in historic parts of Krakow.

All Saints' Day - the day is connected with tradition of visits to the cemeteries in whole Poland. The cemeteries become embellished with flowers and lit with numerous candles - what creates unforgettable view.
Christmas Market - Christmas Market is open already in November (on the main Market Square of Krakow) and offers the locals and visitors hand-made goods, traditional products as well as Polish specialties.

Nativity Scenes Contest - the contest of Nativity Scene is Krakow tradition. The contestants build Nativity Scenes with characteristis architecture - reminding architecture of Krakow. The organiser - Historical Museum of Krakow - gathers the best pieces to make the exhibition.          
New Year's Eve - farewell to one year and welcoming the New one is celebrated on the Main Market Square of Krakow (becoming a huge open-air party).

Websites where one can find Krakow events' calendar: - Krakow Festival Office that organises many events in the city. The Polish version has detailed descriptions of all of them while the English one presents annual events and forthcoming ones. - official website of the city features all-year calendar (unfortunately sometimes not working) and all additional info on Krakow.

Wikipedia on "Events in Krakow" - free online encyclopedia about annual events taking place in the city of Krakow (with short description of each of them).