I was once in your shoes, Bob. Played for years and years without a single effect of any kind. In the last year I've owned several. If you want to start experimenting with them, I think there's some good places to start.
Dirt, fuzz, distortion. This was always a hard one for me. Back in the day I became quite enamored of the clean, full range bass sounds of the 80s. No more of those nondescript fuzzy *bump* sounds for me. It was hi-fi all the way. I was gonna play some slap on cabs with tweeters like Duran Duran. Or something. But what I've come to realize is that there's a big, gorgeous, delicious world of overdrive, fuzz and distortion that's really worth exploring. You can go classic retro like the Tech21 stuff, you can go chainsaw face-melting like Darkglass and you can go Flaming Lips synth sounds like Source Audio. There's a lot to discover in this area. Listen to some youtube clips with headphones on, make some decisions about the basic sounds you like. Do some talkbass research on particular models and then pull the trigger. I wouldn't be caught dead without some grit on my board these days.
You could just decide to drop a funk bomb on your sound and get an envelope filter. These are really fun to play with but I've found they take some courage to use live or in the studio. Your mileage may vary. There's tons of these out there, including a seemingly endless supply of out-of-production boutiques with loyal followers advising you to search for them used on ebay. I myself would just go with the MXR unit. It just nails those classic funk sounds right to the floor. I ended up selling mine to get a wackier, swiss army knife of an EF, the Source Audio BEF Pro--but that's a pedal you don't buy on a whim.
Synth! There's so much synth bass in popular music these days you really can't avoid the subject. To a certain extent I've found that synth pedals are either too flawed, too expensive or both. Your best bets on experimenting with this are probably going to be the BOSS, Behringer (yes!) and Digitech units that you can get from $50 to $150. They seem like good values and you're going to find a few usable sounds on them.
I'm not big on delays and reverbs. I just don't get it. I leave it to others to explain them.
Of course you can't forget more utilitarian pedals like tuners and compressors. Tuner? No brainer. There are a few popular ones. I think they're far more efficient than headstock tuners or even rack tuners. Compression... some people say they don't need it. Others say they won't play without it. I like a very transparent compression that just evens out my level as I change techniques. It's subtle, but once you get used to having it, it's hard to go back.