I noticed a dearth of recommendations for Taipei so I thought I'd share the list I just sent to some friends for an upcoming trip. By no means is this list comprehensive but the places are fairly well known so it's a good start for those who are familiar with Taiwanese food but haven't been to Taipei.
永和豆漿大王 - 復興南路店
I believe they're open 24/7
Recommend: 鹹豆漿, 冰豆漿, 飯團
Note: There are many locations but this one is both very good and tourist friendly.
阿宗麵線 - 西門町總店
週一至週四 11:00 ~ 22:30
週五至週日 11:00 ~ 23:00
Recommend: 大腸麵線 (this is pretty much the only thing they sell)
Note: They have two other locations: 士林分店：台北市文林路101巷24號1樓 and 東區分店：台北市忠孝東路4段17巷2號
洪師父麵食棧 - 建北店總店
週一至週日 11:00 ~ 24:00
Recommend: 紅燒牛肉麵, 清燉白菜牛肉麵, 牛肉乾, 半筋半肉 (you can order this as a side dish)
Note: This place has won various awards for best beef noodle soup in Taipei.
君悅排骨 - 仁愛店總店
週一至週日 10:30 ~ 21:00
Recommend: 排骨飯 (this is pretty much the only thing they sell)
Note: There are many locations but the main branch is one of the most consistent.
週一至週日 11:30 ~ 14:30 / 16:30 ~ 21:30
Recommend: 絲瓜小籠湯包, 蟹黃湯包, 三鮮鍋貼, 大餅捲牛肉, 豆沙鍋餅, 蘿蔔絲酥餅 (it's good only if you are part of the first lunch seating when it's fresh out of the oven)
Note: This restaurant is very close to 杭州小籠湯包 (see below).
週一至週日 11:30 ~ 21:30
Recommend: 乾隆灌湯餃, 小籠湯包, 南瓜糕
Note: This restaurant is very close to 盛園絲瓜小籠湯包 (see above).
鼎泰豐 - 忠孝店
週一至週五 10:00 ~ 14:30 / 16:00 ~ 22:00
週六例假日 10:00 ~ 22:00
Recommend: 松露小籠包 is the new item and it's quite amazing.
Note: I personally think 鼎泰豐 is still the best; this location is not the main branch but the lines are shorter (even though the food is as good).
忠誠山東蔥油餅(此燈亮有餅) - 克強路總店
台北市士林區克強路3號 (near SOGO in 天母)
週一至週日 09:30 ~ 19:30
Note: You can buy 1/4 or 1/2 slice, but if you buy the whole pancake you can request it to be crispier. There are two other locations and the 和平東路店 is open 11:30 ~ 13:30 / 17:30 ~ 20:30.
週一至週日 05:30 ~ 10:30 (三節以外全年無休)
Recommend: 豆漿, 油條, 薄餅夾蛋, 焦糖甜餅, 招牌厚燒餅夾蔥蛋 (the 燒餅 is what they are known for)
Note: This place is very well known so the lines are very long unless you go before 6:00am. It is also open for breakfast only.
Recommend: 奶茶 with your selection of 珍珠, 粉條, 椰果, 仙草, 愛玉
Note: There are many locations (think Starbucks). For more information please visit http://www.50lan.com.