You can cut off the blooms, called deadheading. Most flowering plants will try to complete their life cycle, which is to make more seeds to reproduce. If you cut that activity short by deadheading, most flowers will put out another flush of blooms, trying, as it were, to get to the seed stage. The later blooms may or may not be more prolific than the first. If you want to collect seeds or let the plant reseed itself, then you have to let at least some of the flowers to all the way to seed dispersal stage.
As far as what to plant them with, they are pretty easy going. I have some in a cottage bed of mixed perennials including monarda, butterfly bush, roses, and 2 holly shrubs. I also have a wildflower area which is mostly tickseed and some BE susans. I also have a bed with tickseed, b.e. susan and zinnias. I see them often with coneflowers and daisies too.

Oh, sorry. I answered this question up in Nell's post about the rose and rudbeckia.

Purple spikes of saliva (or veronica) work great with rudbeckia. I also like it with orange blooms.

Cameron

Deadheading will help. They grow fairly easily and are drought tolerant. They will bloom all summer into fall. They reseed like crazy. I find new shoots in the strangest places every year.

I think they go well with anything purple. I had volunteers come up between the liatris, it's a gorgeous mix.

This picture I took early spring {{gwi:649352}}

Edna

Mine keep going with deadheading but I'm not in a terribly hot zone. I will warn you about rudbeckia 'Maxima' - it gets very tall and wide so if you ever try it put it in a large space where it can do its thing. I have one in my front cottage beds that is over 6 ft. More like rudbeckia 'monster'. lol!

Diana

These are mine from last year. 'Prairie Sun' with brown eyes. They did not come back or if they did, they reverted to their native ancestry as they are not the same.
{{gwi:725157}}

Black-eyed Susans are native here in the prairie belt of North America.

This year it came back in the same place, but the blooms are smaller like the native flower - much smaller and shorter. The native's leaves are very fuzzy and produce a lot more irritation than does the cultivor.

Another one found its way over by the potager gate along the garden path and growing out from under a Super Sweet 100 tomato plant that is also a volunteer. The Black-eyed Susan is blooming profusely right now, spilling out into the path. I like it when plants do that. Both seem happy to be companions.

I love them, but like all other sunflower-type plants, I am soooo allergic! I grow them anyway.

These look terrific growing with the old-time native orange day lilies and old-fashioned blue-violet garden phlox.

~ sweetannie4u

Thank you very much. They look soo pretty with purple, I would not have thought to have done that. I also did not realize it would reseed, I think I'll just leave them be so I get more seeds. Thank you for the pic's and combo's ideas!

My blackeyed susan's took over last year, and crowded out my plants, so I pulled them out, and threw them by the road, I now have about 5 feet thick of them...though they do look good with purple..

Holly cow! I had no idea it would get like that....