A good tuner is a nice tool to have, but not always needed. It depends largely on what type or types of antenna you are using and how agile you want to be across a band and between bands.
First thing to note, the term "tuner" is a bit of a misnomer, and a lot of newer hams interpret it to mean it brings your antenna into "tune" to make it work better. In reality. all the tuner is doing is correcting an impedance mismatch between the antenna feedline and the radio's coax port. Your radio expects to see a 50 Ohm impedance at the coax connection, and if that is off from 50 Ohms, you get incomplete power transfer and some of the energy that should be sent as signal to the antenna gets reflected to the radio circuitry and bled off as heat. Do that too much and something in the radio will break, so the tuner is there to protect the radio and ensure a better transfer of power to the antenna.
A tuner can make your life easier, you can have an antenna that's not itself resonant on all the bands you want to work, but the tuner can at least correct the impedance match enough to allow you to use it, even if the antenna isn't exactly resonant there itself, it will still put RF into the air. That means needing less "hardware" in the antenna farm to work more bandwidth.
Or, if you rather, you can get antennas that are themselves resonant on all the bands you want to work and feed them directly with your radio. This usually means more antennas, or using antennas that have discrete components built into their designs that facilitate muliti-band use. This can be a bit more complicated and equipment-intensive, so it just depends how you want to go.
And Gamma made a good point, on some bands like 80M where the whole band is very wide, even a resonant antenna for that band might not give you a good low SWR across the whole thing, and there having a tuner would be nice to "patch up" the match on the far ends of the band.