Here are options for getting to Zagreb by various means and from various parts of Europe!

Flying from the UK & Ireland
Croatia Airlines have daily flights from London Heathrow to Zagreb, year-round
Easyjet have a five times a week service from London Gatwick to Zagreb, also year-round
You can use Germanwings to fly from London Stansted, Edinburgh or Dublin to Zagreb, by transferring in Cologne/Bonn

Flying from Europe
Listed below are a number of direct flights from various European cities to Zagreb. Some routes only operate during summer - please check airlines' websites for full details.

From Austria:
Croatia Airlines flights from Vienna

From Belgium:
Croatia Airlines flights from Brussels

From Bosnia and Hercegovina:
Croatia Airlines flights from Sarajevo

From Denmark:
Croatia Airlines flights from Copenhagen

From France:
Croatia Airlines flights from Paris
Easyjet flights from Paris CDG

From Germany:
Croatia Airlines flights from Frankfurt and Munich
Easyjet flights from Dortmund
Germanwings flights from Berlin, Cologne/Bonn, and Stuttgart (the airline can also be used to reach a number of other European cities by transferring at one of these German airports)
Lufthansa flights from Frankfurt & Munich
TUIfly flights from Cologne/Bonn, Berlin Schonefeld & Stuttgart

From Greece:
Croatia Airlines flights from Athens

From Israel:
Croatia Airlines flights from Tel Aviv

From Italy:
Croatia Airlines flights from Bologna and Rome

From Kosovo:
Croatia Airlines flights from Pristina

From Macedonia:
Croatia Airlines flights from Skopje

From Montenegro:
Croatia Airlines flights from Podgorica

From the Netherlands:
Croatia Airlines flights from Amsterdam

From Portugal:
Croatia Airlines flights from Lisbon

From Russia:
Croatia Airlines flights from Moscow (new for 2012!)

From Qatar:
Qatar Airways flights from Doha

From Serbia:
Croatia Airlines flights from Belgrade (new for 2012!)

From Spain:
Croatia Airlines flights from Barcelona
Iberia flights from Madrid

From Switzerland:
Croatia Airlines flights from Zurich

From Turkey:
Croatia Airlines flights from Istanbul

Bus & Train from Europe
There are international bus services from - amonst other places - Austria (Graz & Wien), Czech Republic (Brno & Prague), Italy (Trieste), Germany (various including Dortmund, Dusseldorf, Frankfurt, Hamburg, Munich, Stuttgart), and Switzerland (Lucerne & Zurich). Routes operated by Croatia Bus.

There are train services from many European cities; you can look up timetable on the excellent Die Bahn website.

From elsewhere in Croatia
As Croatia's capital, Zagreb is obviously very well connected to the rest of the country! By far the quickest way of reaching Zagreb from other parts of the country is by air - Croatia Airlines have flights from Pula, Zadar, Split and Dubrovnik.

Check the Zagreb Bus Terminal website for timetable details of the very many routes to and from Zagreb.

Train routes in Croatia aren't as extensive as bus routes, but Zagreb is the most connected city of all. (Think of Zagreb as the main train hub with routes branching out from it.) The most popular train route is to or from Split; you can also reach Rijeka by train or travel northeast towards the direction of Hungary. See the Croatia Railways site or the Die Bahn website for timetable details.