How long does it take to go from Buffalo airport to Niagara falls in taxi, considering the border?

depending on the time of the day 30-45 mins

I would recommend you allow an hour. It really depends on the day of week, and time of day. If its 4 o'clock on a Friday, you can expect a ton of traffic in the hotel district in Niagara Falls.

It really depends on how backed up the border is. Usually, getting into Canada isn't that backed up.

Which bridge are you crossing?

I would say about 45 minutes to cross the Lewiston-Queenston or the Rainbow Bridge (and add an additional 10-20 minutes if there is a little of a delay)

If you are crossing the Peace Bridge, a little less time.

*It all depends on if the bridge is backed up though

40 minutes maximum.

Make sure you get a taxi that will take you across the bridge.
There are different options like the Peace Bridge or Rainbow Bridge.

Ask the driver to find out what border wait times are like at the different bridges first.

It depends on many things.
1.The security level if it is high it may take a long time (from 30mins- 2 hours!)
2. The day in the week (If it is friday, saturday or sunday it may take along time!)
3. The time of day! Early in the morning (7-10 am and 4-7 pm are usually the busiest times!)
4. It depends on what bridge you are crossing the Niagara
Falls one is usually pretty fast. (It is also new so it is pretty)

Make sure the driver can take you across the border!*
Make sure you have a passport, it will get you across quicker**

No one has suggested this so I have to. Have the taxi from the airport drop you on the US side, then walk across to the border. You'll get across much quicker and you won't have to pay a cab for sitting in a line. It's just a short walk across the bridge so unless you have an insane amount of luggage this would save you some cash and you can pick up another cab once you get thru to the other side.

It's probably only 25 min from the airport to the border but in Nov when we went up there we sat in line on the bridge for a good 20-30 min. Personally I wouldn't want to pay a cab for sitting there like that if I didn't have to.

I'd say reserve an hour, the drive is only like 20 minutes, but you'll probably have a wait at the border, longer wait if the customs official is a dick.