Basic specialist equipment needed for hill climbing – the really most basic base – consists of one item: a pair of walking (hiking) boots. In fact, you can climb many a hill and a surprising number of mountains in trainers – the author of this article recalls hiking up to 2,000m above sea level in the High Tatras in cheap sneakers and well above 1,000m in Carpathians – but even of decent, well marked and maintained paths it's only possible in dry weather and for a fit youngster and even then not advised as particularly sensible.
For climbing ''hills'' (ie nothing that requires serious scrambling, or rock climbing) and general mountain walking (the pursuit also called hiking and tramping in various countries) outside the winter season, lightweight walking boots are sufficient. They should be waterproof (leather or canvas lined with a waterproof, breathable material like Gore-Tex) and offer ankle support, good tread to prevent slips and a sole which has a balance of thickness (for protection) and flexibility (for comfortable walking). Generally, you get what you pay for in hiking boots, but low to medium priced boots will be adequate for most people. The older, the less fit and heavier you are the better boots you need to buy. Brasher (this writer's favorite), Meindl, Scarpa, Alt-Berg, Salomon, Merrell, Hi-Tec (great for kids and budget boots) & Berghaus are all reputable makes.
You will also need – obviously – clothing, but although the world has moved on from the times when Alpine peaks were attempted in plus-fours and tweed jackets, basic hill- walking doesn't require specialist clothing. A waterproof jacket is essential in all but the driest environments, as in most mountains weather can – and does – turn quickly. Depending on the weather and the season, you will start out wth anything from numerous layers to a t-shirt. Modern preference is for man-made fibres that wick moisture away from the body, but silk, wool, cotton and recently popular bamboo have all its advantages, especially closer to the skin. You need enough to stay warm if the weather changes and layers are essential. Polar fleece and its variants is light and can be very warm. Waterproof over-trousers are advised in some areas (Scottish Highlands for example) though are not essential unless on a very long or winter hike. Thick above-ankle socks are required for most walking boots.
A hat or a headband to keep your head and ears warm is important (remember temperature drops as you go up and winds are stronger higher up, on ridges and exposed hillsides). On sunny days, a wide-brimmed sun hat (with straps or elastic to secure it) or a peaked cap are very important: the sun is stronger the higher you go. Sunglasses are also advised for all but the most cloudy locations (and particularly if there is snow higher up as the reflected glare is vicious).
You will also need a backpack (day-pack) to carry spare clothing, water and food. On cold days a flask (thermos) with a hot tea or coffee is an excellent thing to have: nothing is as lovely to behold as a hot drink passed to you as you huddle against horizontal rain and gale-force wind in a marginally more sheltered nook of a rock after bagging a Scottish Munro.
Some items of gear are unessential in certain environments and become absolutely basic in others. A tourist map of the area with paths and terrain marked on it is always good to have, though many hill and mountain trails in Europe for example so well maintained and sign-posted, so a map might not be strictly necessary. In other places (eg Scottish Highlands) a map – as well as a compass – is a must.
And finally, a knife (a good multi-purpose one like a Swiss Army knife is best) and means of making fire in an emergency end the list of the basics.
None of the above (apart from, obviously, the boots) need to be special 'hiking' or 'hill walking' items.
Those going for a hike longer than a half-day should carry a torch (flashlight) and means of making fire . Some very basic first aid kit (plasters, bandage, pain killer, disinfectant) is advisable and in some locations insect and tick repellent will make life much more pleasant. Many people feel better with a whistle to attract attention in the emergency. A fully-charged mobile (cell) phone is worth carrying although many areas won't have coverage – but people have been saved from life-threatening scrapes by being able to make that vital call.