All of the three cars I've had have been slow and some degree of fun. My first was a 1988 Toyota Tercel 3 door hatch with a 78 hp 1.5 and a 4 speed stick. (78 hp when new, I doubt it was making that much when I got it). I think it only weighed about 2000 pounds. Fairly tossable and the suspension was still nice and stiff.
Then I had a 1983 280zx. Slow by today's standards like all the early 80s sports cars were -- 145 hp, 5 speed MT and weighed 2800-2900 lbs. Not fast but RWD with a near 50/50 weight distribution, and had an inline 6. Had enough power/torque that it was fun to push it around turns but not enough to be dangerous.
My current car is a 2007 Civic coupe with 140 hp 1.8l engine, 5 speed MT, 2700 lbs. About as fast to 60 as the 280zx was but less grunt down low so requires more downshifts on the highway (which is part of the fun). Compared with the rest of its class this car is fun to drive, but when compared with older economy car examples it's more comfortable and less like a go-kart. The potential is there, though, and if I have it long enough to wear out the suspension it may get some upgrades.
The wife has a 2008 Mazda3 with the 2.3l 151 hp engine and 5 speed MT. It's actually fairly comparable to the Civic but you can feel the extra grunt in some situations. Its tested 0-60 time is in the low 7s though so it's getting to a point where I'm not sure I consider it slow.