You should know how to create different tones just using your hands. In fact, here's a lesson just on that:
How To Get Different Tones On A Bass Guitar Using Just Your Hands
If you want a variety of rock, metal, pop, and other modern (and classic) tones, you'll need some effects. I just got a Zoom B3N and haven't dived in too hard on it but created this lightening quick video.
Zoom B3N Multi Effects Bass Pedal
This is a relatively cheap bass pedal that you can use live and in the studio. I bought it mainly as a practice tool but it's something I'd definitely consider using in the studio. The tones you can get from it are vast. I haven't tried out anything similar but something like the Line 6 Helix HX Stomp would be great too.
Here are the tones I was going for with a video or song showing the original tone. Note that I spent about five minutes dialling in each tone so I'm sure I can spend a but more time and refine it a little more.
Anthony Jackson first used one of these (played with a plectrum) on For The Love Of Money by The O'Jays.
Flea's intro on the Chili's Around The World is a great example of this common bass effect.
Another very common bass effect used a lot in the '80s and popularised by Pino Palladino probably more than anyone.
This can be used to thicken up the sound and add a sparkly shimmer to your tone. There's a great example on the Journey live album.
Most effects units have decent amp simulations these days which is useful as many gigs are amp-less. You can add one to give a little beef to your current amp set up though, or even to add another tone to your organic amp sound.
Roland Jet Phaser
I've always wanted to make the tone Larry gets in this video. It's full on bonkers! You can't get an original Roland Jet Phaser without selling a kidney. I'm quite happy with the tone I got on my video.
Moog Synth Bass
This tone was used a lot back in the day, usually played by Stevie Wonder or Greg Phillinganes on a mega hit or ten. This is very useful to have on a gig without having to go down the keyboard route.
Buzzy Synth Bass Tone
Another synth bass tone. Loads of pop bass lines don't use bass guitars at all but some kind of fat synth tone. This is one of my favourite lines.
Slap Tone (Compression + EQ)
A good basic slap tone is worth having. The Sadowsky preamp pedal is a great option to get that Marcus Miller tone but I managed a decent tone using compression and EQ to level out and fine tune the tone.
Tim Commerford's bass tone is a closely guarded secret but it's mighty, that's for sure. I went with some fuzz/distortion and some octave blended in.
I love delay on bass but it's not used an awful lot in songs. This is, however, a brilliant example.
A common bass effect especially in funk. The Zoom has quite a few models to choose from.