Crypto weaknesses are always possible. But generally speaking, widely-deployed algorithm like SHA256, ECDSA, etc (which Bitcoin relies on) don't become suddenly broken one morning. Research progresses slowly (eg. weaknesses found in round-reduced versions of these algorithms), giving ample time to the community to plan for an upgrade when it becomes clear that one of the algorithms will become broken soon.
Bitcoin is also very conservatively designed. For example an address is computed with a RIPEMD160 hash of a SHA256 hash, so one would have to break both algorithms with preimage attacks to be able to generate address collisions allowing an attacker to steal coins from an arbitrary address. Because of this conservative design, it gives it a "safety cushion" to have time to anticipate cryptographic changes if they are needed.
Bitcoin is also very conservatively designed. For example an address is computed with a RIPEMD160 hash of a SHA256 hash, so one would have to break both algorithms with preimage attacks to be able to generate address collisions allowing an attacker to steal coins from an arbitrary address. Because of this conservative design, it gives it a "safety cushion" to have time to anticipate cryptographic changes if they are needed.