Is there a way to find deep holes (fishing holes) in rivers without using a depth finder?

Look for slow moving areas of water. Or a calm spot in the river...this indicates a significant drop off where the water slows down and is allowed to pool. Also, as the other person said the outside bend of rivers tend to be deeper than the rest of the river.

Zoom into the section of your river with maps.google.com. Sometimes you can see the holes in aerial view. Where rivers bend, the current follows the outside path and carves a deep channel - usually the sharper the bend the deeper the groove. The hole usually extends past the bend and it is often even deeper there. If your river has break walls, bridge pilings, or permanent sand bars they usually drop into deep holes just down current. Also, the farther downstream you go in most rivers, the deeper it gets. For deep water species like cats and walleye this is a good way to find them. By the way, you can probably find a used canoe for 200 bucks or less, especially if you check with canoe float companies if they have any older canoes they're trying to get rid of. No need to register or pay taxes on it in many states if you don't have a motor, and you can strap it to the roof of your car. If you have waders and a pair of scuba/snorkeling fins, you can get a float tube for 50 bucks and either way will get you into a lot more fishable water (assuming your river is safe enough for either).

darker water is normally deeper... it is normally deeper in eddies... or drop banks... once you've fished flowing water for awhile you'll get to know what deeper spots look like... fishing smaller streams will help you understand the way streams beds and river beds generally are... the holes are often similar in bigger rivers...

Throw out a heavy jighead and count how long until it hits the bottom.

no, try using a slip bobber with just a sinker, and search for deeper spots with that. keep adjusting your slip tie a foot until your bobber sits on its side. then set your slip tie a few feet deeper and search around. thats all i can think of.

Throw out a heavy weight with a light bobber tied at about what ever length you think is right if the bobber sinks then you have hit deep water. Also, the darker the water, the deeper, Maybe you could find a long branch and poke around a bit. If all that fails I suggest that you hop on in and test it out.