The answer is the discone antenna, widely used on VHF and UHF.
It's quite a big beast comprising a disc at the top and a cone at the bottom (hence the name). Although more often than not it's not a real disc and cone. Instead it's lots of elements radiating from the feedpoint to form what amounts to be the same thing electrically. They also often have a vertical element for lower frequencies.
At first sight the discone doesn't sound very attractive.
But if you want a general purpose wide band vertically polarised antenna for listening and local transmitting, then the discone could be just right.
If you've got a RTL2832 software defined radio dongle you probably got a short vertical antenna maybe 15 or 20cm high. They're useless. You might hear local FM broadcast stations if you're lucky. An outdoor discone fed with coaxial cable will be far better and allow you to receive a wide variety of VHF/UHF transmissions including aircraft, broadcast, amateur and more. In fact the discone has had a big surge in popularity since SDR dongles came out and people wanted an antenna that suited their dongle's wideband receiving capability.
What about transmitting? They're not better than a dipole or ground plane. But their broadband capability is particularly useful in countries like the United States with many VHF/UHF amateur bands, for instance around 50, 144, 222, 432 and 902 MHz. You should be able to comfortably work through repeaters up to about 50km away with 5 to 20 watts output power on FM. Just make sure your transmitter's RF output is clean because if it isn't the discone will faithfully radiate any spurii due to its broadband nature.
You will need a stout solid mast to mount a discone. Particuarly one that operates much below 100 MHz. But if you've got lots of scrap metal, for example from an old TV antenna, the cost to build one is not high. They make a great reference antenna that provides a base level of performance against which you can compare your higher gain verticals and beams. If your other antennas are performing worse than the discone then you know something's wrong.
Here's some ideas for homebrew discones:
* Home made coat hanger discone
* Instructables discone plans for SDR
* WB4HFN notes on discones
* DIY folding discone (video)
PS: Want to read more about antennas? Consider this selection of antenna books. They are affiliate links meaning that I receive a small commission (at no extra cost to you) if you decide to purchase.