I'm currently using a 21" monitor as an external monitor on my MBA. It's about 5 years old and it's beginning to get restricting with the amount of space I have when developing.

The resolution of it is 1680x1050.

If I go for a new monitor what is a current good resolution for 21" monitors? Or should I look at something bigger 24"?

Can anyone recommend a brand/model?

21/22" displays are likely to have the same resolution as you've currently got or the slightly higher Full HD (1920 x 1080).
Stepping up to 23" and it's most likely you'll only see the Full HD.
If you can stretch to 24" then you get a choice of Full HD or the more old school (and better IMHO) 1920 x 1200.

Personally I'd try and go for a 1920 x 1200 24" IPS display if you can afford it.
HP and Dell both offer pretty decent displays (look for the ZR and Ultrasharp ranges respectively) with a good mix of colour reproduction and price. Stepping further up the range if you do a lot of colour critical work you've got the likes of NEC (Multisync P, PA and SpectraView ranges) and for proper bonkers prices you could have a look at Eizo (Flexscan and ColourEdge ranges).

I've got a NEC MultiSync LCD 2090UXI (4:3, 1600 x 1200) display at the moment and if I was looking to replace it I'd probably take a look at a 24" Dell Ultrasharp to start with as they usually perform quite well in tests especially once properly calibrated.

Thanks! The ultrasharp looks awesome!