MinnMan

It depends where I'm going and for how long. Sometimes I bring my bike, sometimes I rent. I agree with what people already said about fit, but I've had some very nice rentals at times. There are places where rentals are easy, but at times getting to the rental place or shop is a major logistical hurdle. And at times, expensive.

Places I've rented bikes. Maybe I'm forgetting one or two. I'm not naming sources here, but all of these were found with google searches, mostly easily.

San Francisco - many times - bike shops at Fisherman's Wharf mostly rent cruisers, but a few have OK road bikes. Ride across the Golden Gate and the world is your oyster.
Santa Barbara - high end bikes available for long-term rentals at reasonable prices.
Las Vegas - very easy to rent a good bike
Houston - nice bikes available from the local big lbs chain, but pricy.
Northampton, MA - nice bikes from an LBS.
Catania, Italy - Nice Pinarello from an LBS a few blocks from my hotel, at surprisingly cheap rates
Oxford, England - was surprisingly hard to find a bike to ride. Found a cross bike for an afternoon.
Ronda, Spain - excellent bike - rental service delivered to my hotel
Girona, Spain ditto.
Lisbon - Had a hard time finding a bike, but partly b/c it was off season. Managed to rent a cx bike for a day and had a nice ride.
Berlin - dead easy to rent a city bike, harder to rent a road bike and a little expensive, but possible. I've done both.
Vienna - easy to rent a MTB and ride along the Danube. Didn't try to find a better bike. Might be a challenge.
Quito, Ecuador. No way to rent a road bike, but with those roads, a MTB was a better choice anyway.
Banos, Ecuador. ditto - and very cheap.

Edit: Almost forgot:
NYC: Hybrid bike for riding along river from an LBS in midtown. Not a bad way to spend the afternoon and better than a citibike.
Nassau County, Long Island - a couple of different LBS rent MTB or cross bikes. Couldn't find a road bike. Somewhat expensive.