Depends on how much you know the car.
2 summers ago I did a 9000mi. cross country trip in a 1998 BMW with almost 200k on it. Not a problem.
Of course I had owned the car for 2 years and did all the maintenance and update on it myself, so I was pretty sure it was good to go. If you know little about cars or the maintenance and repair history, you could be out of luck and should probably have AAA.
Depends on how long and how far you're going. . .
1. Short and frequent- So if it was a bunch of short (300 mi. or so) road trips, as long as you know it's maintained and have AAA, take as many as you want.
2. Long and epic- If you are planning a concentrated road trip of a few thousand miles and a few weeks, just rent a car and take advantage of that wonderful thing called "unlimited miles". Make them regret the offer!
3. Regular vagabonding for years (hundreds to thousands of miles whenever you feel like it)? Just get something they made millions of, made for durability and not style or mpg, and dead simple to repair. If you're up for it- get a manual transmission. I'd wager at least 50% of older cars are left for dead because of neglected auto transmissions that are too expensive to be worth the repair.
For starters, mostly trucks because they are built simple for work and are way overkill for anyone who doesn't use them for actually hauling anything. Half a million miles is a reasonable expectation before any major component repair if properly maintained. Like:
-Jeep Cherokee- Brilliant vehicle. Had one, loved it, but they get rusty in the salt belt. Owned one for 8 years. Grand Cherokees from that era that are lower spec (usually the 6-cyl "Laredo" model) are similar in reliability, but bigger.
-Toyota/Nissan pick up from 1980s-1990s- Tin cans made to run forever. Higher than necessary resale prices in some markets, though.
-Ford Ranger/Mazda B-Series- Current daily driver. They literally sold millions of them, and only slightly updated the design over the years. Possibly the least sexy yet most practical and cheap vehicle ever. So if your market up-prices the foreign trucks, these are a relative steal!
-90s full-size pickup truck or van- F-150, Silverado, Dodge Ram- See above, but add 30% more volume (and less mpg)!
Car(ish) vehicles-
-1990s Toyota/Honda cars- Pick your size and go. Civic/Corolla, Prelude, Camry, Accord. Whatever. Just drive them. Smart buy is the 90s Chevy Prism- Corolla with a Chevy badge!
-1990s-early 2000s Pontiac Vibe/Toyota Matrix- Manual transmissions had some issues, so this might be only one of the cars I'd recommend an auto.
-Ford Crown Victoria/Mercury Grand Marquis- Built body-on-frame (like trucks) and were the workhorses of Police departments and taxi services for a reason. They actually get over 25mpg highway, too!
-1990s-early 2000s Buick- Regal, LeSabre, etc. Believe it or not, these have reliability similar to Toyota/Honda of the same era, yet drastically lower resale prices. They also tend to be owned by people who maintain their cars.
For the win (honorable mention with style points)
-Any Saturn built before 2002- Damn plastic wonders! Reliability is similar to foreign models above, but are way underrated.
-Volvo 240/740 series. Seriously overbuilt vehicles. As long as correctives have been made for problems in certain models, they will probably outlive you.
Yes, there are cars built after the early 2000s that are good, but they tend to suffer from trying to meet too many requirements (comfort, safety, emissions, mpg, style, etc.) and tend to get overcomplicated. Remember, sexy is your enemy!