Brown as in turning into wood is OK.

Brown as in looking slimy means too much water, not enough drainage.

Start worrying when both the stem AND the leaves are brown. That means your plant is dead (or nearly dead).

I love daisy's answer, right on. If it's turning to wood, I would cut it down a bit to encourage more bushy growth, but that's probably a personal preference. I have always thought that as basil got woody the production decreased, so I try to keep them cut enough to prevent getting too woody. It also depends on how much more time you have if before frost kills it. If its just a bit more then let it be cause you wouldn't have enough time to get more shoots.

I felt the base of the plant and it does indeed feel woody. it's getting rather large and I've been pinching off flowers like crazy. I think I'm going to make a boatload of pesto this weekend and cut it down that way!

I will say this about it, though: I noticed last night that the leaves are curling a bit, much like my tomato plants did once- i think from underwatering? (or is it overwatering?? oy...) I put a wick in the pot last night at the recommendation of someone who knows a LOT about drainage, so I'm hoping it will allow me to water the basil daily and still keep it well drained. If it sounds like I'm misunderstanding any part of this process, please let me know!!!

Thx- Anne : )

The wick thing is an interesting idea.

But, I don't understand why you need to water daily. You can check plants daily (I'm lazier than you though), stick your finger in the soil upto the first knuckle atleast , if it is damp walk away. If it is significantly dry, add water thoroughly (hopefully the plant has drainage holes). I guess your in an arid region but unless the plant needs water (soil is dry) I don't water them. Herbs especially to be too wet. The only time I need to water daily is if it's really hot and usually when my plants are in too little containers. Get bigger containers, with drainage holes (I like terracotta pots), and use some sphagnum moss (cause it looks pretty-any mulch will do) to help retain the waer. Then they won't dry out as fast, you can still check daily but only water when necessary.

My basil plant has the same wooden effect crawling up from its base. However, one of the main columns of the plant is becoming increasingly limp in comparison to the main bulk of the plant. It looks like it will surely die. Should I remove this column?