Does the thought of a digital SLR scare you? Do you want a long zoom without the hassle of interchangeable lenses?
It sounds like you need a superzoom camera. Superzooms are characterised by their SLR-like styling, but are generally more compact and boast optical zooms that can range all the way up to 50x.
You might also see these sorts of cameras termed as "bridge" or "megazoom" cameras.
What to look for
The advantages that superzooms have over conventional long-zoom compacts is that most of them have manual controls for fine tuning your photos. Some manufacturers also have a range of fun accessories that you can buy, such as filters and external flashes that can simulate the shooting experience of an SLR without the bulk.
Image stabilisation is standard on superzoom cameras; however, for the best results, particularly when you start to reach the upper echelons of zoom, you will need to invest in a tripod to avoid camera shake.
Full HD video recording is standard on pretty much all new cameras, but it's definitely worth checking to see whether you can attach extra accessories, like an external stereo microphone to improve sound. The Panasonic FZ150, for example, has a jack into which you can plug another microphone.
Rechargeable lithium-ion batteries are standard fare on superzooms; however, if you value AA batteries, check out a model like the Nikon Coolpix L810, or the older model, the L120.
Want something smaller? You might be interested in compact cameras with big zooms.