To be honest? Usually not
There are loads of photographers that won't agree, but I genuinely believe that you just don’t need two photographers at your wedding. Most of the time one photographer is more than enough to capture your wedding day. I am there with you all the way from prep through to the reception and photograph everything as it happens and having your whole day captured by the same person means consistency in both shooting and editing style.
But won't two photographers mean I get more photos? Again usually not, and if there are then they'll be just documentary photos of what's going on, similar to that which your guests will be taking. Trust me, you don't want thousands of average photos of your wedding day, getting a slightly smaller gallery of higher quality images is always better!
That being said - there are 3 times when a second photographer is both beneficial and will add to the day rather than be in the way.
You want both partners prep covered & you're in different locations
This one is quite self explanatory . Your photographer cannot be in two places at once so if you want full coverage of the both of you getting ready then two photographers is the way to go, especially if you're getting ready at different places.
If you're both getting ready at the venue, just in separate rooms, then I can usually make it work to cover both of you without the need of a second photographer. I'm an over-planner so will bounce back and forth between your rooms around what time important things will be happening
You want 2 perspectives on your whole ceremony
If you already know you want your ceremony covered from different angles then you'll probably already be thinking of booking a second photographer and I do agree on this one. It is nice to be able to get two perspectives on the ceremony, especially if you're getting married outdoors with a view. Bear in mind though that a second photographer will usually get very samey shots throughout the whole ceremony as your main photographer will be upfront with you capturing all your expressions.
You have over 200 guests
Having a lot of guests and only one photographer can mean that some people may get missed - it is much easier to document a large wedding with so many guests when there are 2 of you to divide and conquer!
Anything under 200 though? That can easily be covered with just one person, especially if that one person takes the time to get to know you and who is important to you.