I love his salads.
Don’t forget Ross Creek, a less-known tributary of the Mighty Guadalupe. 
Once upon a time, when Eisenhower was POTUS, I traced most of Ross Creek’s path via bicycle. IIRC, there were several points at which the Creek was no longer visible, passing through drain pipes.
As a youngster I spend many hours playing near that Creek – though I don’t know if we even knew its name – watching polliwogs, etc. Thanks for bringing it up; I’ve rarely even thought of it in recent decades.
Can’t say that I pay that much attention to rivers as I cross them, unless they’re picturesque. Australia doesn’t have too many, compared to most countries, what with them mostly being slick sludge or completely dry, but the main river in this town is the Yarra, and I expect I crossed it sometime recently as it snakes its way through most of the suburbs near me. I was certainly right beside it just a couple of days ago, though I didn’t actually cross it then.
Ditto.
The Charles. Almost every single weekday. Sigh.
The Brazos. Just up river my friend Greg’s ranch has a low limestone outcrop used first by Indians to cross the river in flood. Sam Houston later used it as he lured Santa Anna and his army toward San Jacinto. Custer camped there with his men and it’s the site of the long lost Bernardo Plantation. We’ve found arrowheads and mastadon teeth there. All sorts of history there because of a little bit of geology.
I cross two major rivers every day on my commute. First the White River in Vermont, and then the Connecticut River, which is the border between Vermont and New Hampshire. I’m one of those weirdos who live in one state and work in another. So, since I’m at work, most recent is the Connecticut, about an hour ago.
I crossed the Scioto River yesterday. It flows through the town I live in.
St-Lawrence River at least twice a day sometimes 4… I do have to get into Montreal for work. I mostly cross it by bus or car but sometimes by metro!
Ditto that. But only to get to the Pollo Tropical as there isn’t one on the Fort Misery side 
Favorite song about crossing rivers:
Alan Parsons Project One More River to Cross
The Schuylkill river last Friday, I believe. I thought the Brandywine on Sunday, but technically not a river at the point I crossed it.
The Catawba, while coming back from South Carolina.
I bicycled over the Mississippi river on the way home from work today
Brian
The Sacramento, just a few minutes ago on my way home.
The Tank Stream - usually at least twice a workday, possibly more often because since they buried it I’m not exactly sure where its course is.
I crossed the Wabash yesterday, but I wished I hadn’t because then I could have said that the Main was the last, with the Rhine being next to last.
I drove over the Marquam Bridge yesterday, so the Willamette River for me. I’m on vacation; I can’t think of any real rivers in San Jose that I cross with any regularity. Are we counting creeks?
I cross the Concord River twice a day on my work commute. Fairly anemic as rivers go, but pretty well known apparently.
The Wisconsin River (the hardest working river in the country based on the number of hydroelectric plants.) This morning and every morning I go to work.
I just spent yesterday on the Megabus from Kansas City to Chicago, so I’m pretty sure my answer is “a lot of them”. Definitely the Missouri and the Mississippi. Heck, I cross one canal and two branches of the Chicago river just getting home from Union Station.