There's a wealth of things to do in Argentina
so what you bring largely depends on what you have planned. In terms of clothes to bring, if you're visiting Argentina during the winter you will need warm jumpers and jackets, particularly in the south of the country where the cold is extreme. Many people think Buenos Aires and the north of the country are warm all year round but this is a myth so make sure you pack for all eventualities, especially if you're visiting in the spring/autumn when the weather can be changeable. Summer is generally very hot in the central and northern regions of the country so bring plenty of sunscreen, a hat and lighter clothes. Most items required by the traveller can be purchased in Argentina (principally in Buenos Aires and other urban areas); however, imported goods are very expensive - in particular, electronic goods and imported foods. If you want to read in your native language it's also worth packing some books, as it's quite hard to find literature in a language other than Spanish.
It's nice to bring a few typical things as gifts for people you will meet in Argentina. For example, chocolate from Europe or tea from England goes down very well. Make sure you bring a Spanish dictionary and/or a grammar book from your country, a good guidebook and relevant plug adaptors (information for each country is usually available online with a quick web search). Insect repellent is worth bringing as well as there are some problems with dengue fever in certain areas of the country. Finally, consider bringing several credit/debit cards as you may lose one during your stay and it's worth arriving with a few US dollars as reserve finance.
If you plan to go hiking or do other activities in the interior of Argentina you should bring appropriate outdoor clothing and equipment - suggestions include warm layers (sweaters and socks), waterproofs, a large backpack and sturdy walking/hiking boots. If you're planning to do other extreme activities you should seek more detailed information from tour/excursion operators. Make sure you check the travel advice in your guidebook regarding infectious diseases in Argentina and bring appropriate precautionary measures (for example, malaria exists in the northeast of Argentina and you will more than likely need medication).