You have tons of options!Exposure is important,so I'll list things both for sun and for shade.For sunny positions,
there are a few different types of Bidens that cascade very well,and look great with other trailers like Lobelia erinus and Calibrachoa.The 'Profusion' strain of Zinnias work well in containers,and will quickly grow to fill them.
Careful about using mixed colors of these,some won't match each other.There's an amazing Verbena,'Imagination',with vivid purple flowers that trail very nicely.And remember the Wave Petunias...good color ranges but rather expensive for annuals.For shadier spots you have some good reliable choices- Coleus can't be beat with the many different colors to choose from,quickly filling pots and tumbling down the edges.Bacopa 'Gold n Pearls' is another good option for shade and it has really neat chartreuse and variegated leaves.The white flowers on them is definitely a bonus!Cascading Fuchsias will mix well with any other type of shade plant,especially Ferns.Tuberous Begonias take a while to get going,but are well worth the wait for their large vividly colored blooms.Lastly,I'd like to mention Browallia.
Blue flowers are somewhat rare in shade plants- this one sports a deep luscious blue.

Shelli,

Some people use petunias for cascading, but the better cascaders that I have seen are Million Bells or Calibrachoa. I don't think you can grow them from seed, but they are available as plants at various garden centers and nurseries. There is also a cross between petunias and calibrachoa coming into the market, but so far with a limited number of colors.

ZM

There is a 'climbing' nasturtium in seed form that they suggest to plant to meander along walls & over patios. Apparently its tendency is to 'trail' rather than climb...not sure why they call it a climber.

I'm a petunia lover, although I use them rarely...what's up with that?? I found a lovely "Cascade" series 2 years ago that was great. I think it was called "Double Blue or Double Purple." The series was definitely Cascade, though.

Morning Glories- some will say these are invasive, but I don't have that problem here in my Z5 yard. I am trying the lower-growing varieties this year: Ensign, Flash, and Enchantment. (Possible they are all the same, only named different depending on what packet brand you're looking at)
The other varieties grow 'up,' not 'out.'

That's all I have for now; I don't typically use trailers much.

Licorice plant can be quite striking in containers, either on its own or as cascading edging. A public building in my town put lots of it, and only that, in their planters one summer and they were gorgeous.

Also depends on just how much of cascade you want. For me allysum does cascade once it gets "big" (which in this case is over 4" tall) though not nearly to the extent that the others mentioned above will. A plus to allysum -- if in strong sun & well watered -- it will really pump out a wonderful honey fragrance.

I had some 'butterfly impatiens' last year that were awesome (and rooted very easily in the fall to keep for sping)