If you are planning a wedding and know that most members of this wedding party are hams who won't mind the whole "public speaking" thing, then by all means keep the toasts traditional with dad, the best man and others taking their expected turns at the microphone.
But if you're looking for something different, either because you want to save putting people on the spot, or you simply want to do something different and fun, read on.
First, you can certainly take the whole toast thing off the agenda if you wish. There are no rules requiring a toast at any wedding. Weddings should be unique events and reflect the personalities of the bride and groom.
But if you want to do something a little different, there are options. You can go the video route, which asks people to essentially make a toast on camera and then the video is given to the bride and groom later. This isn't a particularly unique idea, but it does solve the issue of not wanting to put people on the spot and still gives everyone a chance to say something special to the bride and groom.
If your guest list includes many outgoing people then consider "pass the microphone". This can work in several ways. You can either be silly with it, or deadly serious. Most people like silly. Say dad takes the microphone first. His last name ends with T (so, let's say dad's last name is Smith). He must find someone whose first name begins with a T (Tom? Tony? Tina? Theresa?) and pass the microphone to that person, who then gives a toast.
This method of giving toasts does put people on the spot (certainly before the fun begins you can warn them so if they are really uncomfortable, they can escape to the restroom or bar) but it can also be a lot of fun. Getting people when they least expect it and then asking them to remember something funny or meaningful about the bride and groom can result in interesting, funny and truthful results.
You might also decide that one person at each table be required to give a toast. Number the tables and at various intervals, have the MC or DJ call a number, which will require guests at that table to decide amongst themselves who will give the toast at that table. Certainly, more than one person can if they like, but there will likely be at least one ham at each table who will enjoy standing up and toasting the newlyweds.
Say you have plenty of public speakers in the group, and finding willing toast participants won't be a problem. But you think the subject matter might be. There's an easy solution to this problem. You can provide open-ended topics for the toast speakers. Say you are providing an "open mike" toast arrangement, where anyone can request the microphone and offer a toast. The DJ, MC or someone else in the wedding party (perhaps the maid of honor or best man) can offer the speaker a surprise topic, which might be pulled from a champagne flute or drawn out of the floral arrangement on the head table. There might be slips of paper to choose, or just one sheet of paper with several ideas.
The speaker might choose to finish this sentence, "I remember when (groom's name here) was a little boy, he always ..." or answer this question, "When was (insert bride's name here) at her silliest? Tell us the story". You might have to give each speaker a minute or two to collect their thoughts, but you're sure to have some interesting stories, some unique anecdotes and some different perspectives on the bride and groom.