The Bussard ramjet idea could very well work - if you plan your route correctly.
You're worried about the low number density of hydrogen atoms/ions in outer space. This table shows that this is indeed quite a big problem. There is a solution, though, which is to travel nearly exclusively - when possible - through molecular clouds. These are swaths of space filled with hydrogen and helium where stars are born. They also have a very atomic/ionic number density - roughly $10^2-10^6$ atoms per cubic centimeter (which translates to $10^8-10^{12}$ atoms per cubic meter). Wikipedia says that ~$\text{91%}$ of the interstellar medium is hydrogen; molecular clouds could have an even higher percentage. I'll go with that, and assume a density of $10^{10}$ atoms per cubic meter.
You're on a generation ship, so it's most likely large - after all, it needs to have enough supplies (not just food) to last for many decades. So attaching a large scoop to the front of it shouldn't cause a substantial structural problem. Let's say that the scoop is circular, with a one-kilometer radius. That translates to an area of $1,000,000 \pi$ square meters. Assuming you're traveling at a nice clip - say, $20$ kilometers per second. That means that each second, your scoop travels through $20,000,000,000 \pi=2 \pi \times 10^{10}$ cubic meters of space. With $10^{10}$ atoms per cubic meter, you've scooped up $2 \pi \times 10^{20}$ atoms in that second. If ~$\text{91%}$ of those are hydrogen atoms, you've picked up $5.718 \times 10^{20}$ hydrogen atoms. With one hydrogen atom having a mass of one atomic mass unit ($1.661 \times 10^{-27}$ kilograms); you pick up $8.601 \times 10^{-7}$ kilograms of hydrogen. So it will take you about $115$ days to collect one kilogram of hydrogen.
Fortunately, most Bussard ramjet ideas have much larger scoops. To collect one kilogram of atomic hydrogen per day, you'd only need a scoop with a radius of $10.7$ kilometers. In an answer here, user23660 said that approximately $\text{0.0037681%}$ of the mass is converted to energy. So you have $0.0037681$ kilograms of hydrogen. Via $E=mc^2$, that translates to $3.387 \times 10^{14}$ Joules (using $c=299,792,458$) produced each day, or a power output of $3.920 \times 10^{10}$ Joules per second.
In that one second, $3.920 \times 10^{10}$ Joules of energy have been consumed. The velocity I gave before was $20$ kilometers per second, so the ship has gone $20,000$ meters. Work is defined as $\text{Force} \times \text{distance}$; setting the energy used as work, I get a force of about $195,984$ Newtons. Given that the mass of the ship is $\text{something very large}$, you're not going to have a huge acceleration. You can always increase the size of the scoop: multiplying the radius by $x$ will multiply the area by $x^2$, and thus multiply the amount of hydrogen collected by $x^2$, so long as $x$ is in meters.
Of course, there are ways around this. For example, maybe your ship is propelled by a solar sail. A solar sail takes a while to get to a decent cruising speed, but it needs no fuel. Plus, it will be about the same size as the scoop, so the scoop shouldn't cause any additional drag. This means that all the energy can go towards keeping the ship's inhabitants alive.
Molecular clouds aren't easy to come by, though. Wikipedia (the molecular cloud article) says that they only compose one percent of the total interstellar medium. Ouch. However, it does say this:
The bulk of the molecular gas is contained in a ring between 3.5 and 7.5 kiloparsecs (11,000 and 24,000 light-years) from the center of the Milky Way (the Sun is about 8.5 kiloparsecs from the center). Large scale CO maps of the galaxy show that the position of this gas correlates with the spiral arms of the galaxy.
So you can think of that ring as an express lane for Bussard ramjets. I haven't been able to find an image showing the location, but this (paywalled) paper seems to be a good start. In summary: choose the right locations (and take a solar sail along for the ride) at it seems like you'll be okay with a Bussard Ramjet.
I just realized that there's a loophole to this (and I feel stupid for not realizing it before!).
The Swiss plane Solar Impulse aims to circumnavigate the globe. One of the problems, though, is that it must fly during the night, where there's no solar energy to be gathered. Solar Impulse solves this problem by gathering extra energy during the day, storing it in batteries, and using it slowly at night, while drifting down a little. The ramjet could do this, too, collecting excess hydrogen and storing it in tanks. The fuel would add extra mass, but it would enable the craft to go to new places along new routes.
